Lesson 6.1 Skills Practice Name_________________________________________________________ Date__________________________
Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem
Vocabulary Match each definition to its corresponding term. 1. A mathematical statement that can be proven using definitions, a. diagonal of a postulates, and other theorems.
square
2. Either of the two shorter sides of a right triangle.
b. right triangle
3. An angle that has a measure of 90° and is indicated by a
c. Pythagorean
square drawn at the corner formed by the angle.
4. A series of steps used to prove the validity of an if-then
Theorem
d. right angle
© 2011 Carnegie Learning
statement.
5. A line segment connecting opposite vertices of a square.
e. theorem
6. If a and b are the lengths of the legs of a right triangle and c is
f. leg
the length of the hypotenuse, then a2 1 b2 5 c2.
7. A mathematical statement that cannot be proven but is
g. postulate
considered to be true.
8. A triangle with a right angle.
h. hypotenuse
Chapter 6 Skills Practice • 533
Lesson 6.1 Skills Practice
page 2
9. The longest side of a right triangle. This side is always
i. proof
opposite the right angle in a right triangle.
Problem Set The side lengths of a right triangle are given. Determine which length is the hypotenuse. Use the Pythagorean Theorem to verify each length. 1. 9, 12, 15
2. 10, 26, 24
The length of the hypotenuse is 15. 92 1 1225 152 81 1 144 5 225 225 5 225
4. 6, 8, 10
© 2011 Carnegie Learning
3. 20, 12, 16
534 • Chapter 6 Skills Practice
Lesson 6.1 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 5. 25, 15, 20
6. 15, 36, 39
Calculate the length of the hypotenuse of each given triangle. 8.
7.
14 24 48
18
2 5 a2 1 b2 c
© 2011 Carnegie Learning
2 5 2421 182 c 2 5 576 1 324 c 2 5 900 c ____
c5√ 900 c 5 30
Chapter 6 Skills Practice • 535
Lesson 6.1 Skills Practice
9.
page 4
10.
1.5
9 2 12
11.
12.
6 18
10
© 2011 Carnegie Learning
5
536 • Chapter 6 Skills Practice
Lesson 6.1 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ Answer each question using the scenario. 13. Clayton is responsible for changing the broken light bulb in a streetlamp. The streetlamp is 12 feet high. Clayton places the base of his ladder 4 feet from the base of the streetlamp. Clayton can extend his ladder from 10 feet to 14 feet. How long must his ladder be to reach the top of the streetlamp? Round your answer to the nearest hundredth.
12 ft
4 ft
2 5 a c 2 1 b 2 2 5 4 c 2 1 1 22 c2 5 16 1 144 2 5 160 c
© 2011 Carnegie Learning
c < 12.65 Clayton must extend his ladder about 12.65 feet.
Chapter 6 Skills Practice • 537
Lesson 6.1 Skills Practice
page 6
14. Jada is helping to build a swing set at the community park. The swing bar at the top of the set should be 8 feet from the ground. The base of the support beam extends 3 feet from the plane of the swing bar. How long should each support beam be? Round your answer to the nearest tenth.
8 ft
© 2011 Carnegie Learning
3 ft
538 • Chapter 6 Skills Practice
Lesson 6.1 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ 15. Perry wants to replace the net on his basketball hoop. The hoop is 10 feet high. Perry places his ladder 4 feet from the base of the hoop. How long must his ladder be to reach the hoop? Round your answer to the nearest hundredth.
10 ft
© 2011 Carnegie Learning
4 ft
Chapter 6 Skills Practice • 539
Lesson 6.1 Skills Practice
page 8
16. Ling wants to create a diagonal path through her flower garden using stepping stones. She would like to place one stone every 2 feet. How many stepping stones does she need?
12 ft
© 2011 Carnegie Learning
16 ft
540 • Chapter 6 Skills Practice
Lesson 6.1 Skills Practice
page 9
Name_________________________________________________________ Date__________________________ Calculate the length of the missing side of each given triangle. 17.
15
6
18.
22
24
c25 a2 1 b2 1525 62 1 b2 225 2 36 5 b2
19.
4
189 5 b2 13.75 < b
8
20.
5
© 2011 Carnegie Learning
7
Chapter 6 Skills Practice • 541
Lesson 6.1 Skills Practice
12
21.
page 10
22.
8
14
18
23.
8
24. 6 10
© 2011 Carnegie Learning
3
542 • Chapter 6 Skills Practice
Lesson 6.2 Skills Practice Name_________________________________________________________ Date__________________________
Can That Be Right? The Converse of the Pythagorean Theorem
Vocabulary Write the term that best completes the statement. 1. The
states: If a2 1 b2 5 c2 , then the triangle is a right
triangle. 2. The
of a theorem is created when the if-then parts of
the theorem are exchanged. 3. A set of three positive integers a, b, and c that satisfy the equation a 21 b2 5 c2 is a(n)
.
Problem Set Determine whether each triangle with the given side lengths is a right triangle. 1. 8, 15, 17
2. 6, 9, 14
c25 a2 1 b2 1725 1521 82 289 5 225 1 64
© 2011 Carnegie Learning
289 5 289 This is a right triangle.
Chapter 6 Skills Practice • 543
Lesson 6.2 Skills Practice
page 2
4. 5, 12, 13
5. 6, 8, 10
6. 9, 12, 16
© 2011 Carnegie Learning
3. 12, 15, 18
544 • Chapter 6 Skills Practice
Lesson 6.2 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ Answer each question using the scenario. 7. A computer monitor is sold by the diagonal length of the screen. A computer monitor has a 15-inch screen. The screen has a width of 13 inches. What is the height of the screen? Round your answer to the nearest tenth. 2 5 c 2 a21 b a21 1 325 1 52 a2 1 169 5 225 a25 56 ___
a5√ 56
a < 7.5
© 2011 Carnegie Learning
The height of the computer monitor screen is about 7.5 inches.
Chapter 6 Skills Practice • 545
Lesson 6.2 Skills Practice
page 4
8. Luisa is building a sand box in her backyard. She places four pieces of wood in a rectangle to form the frame. The rectangle is 4 feet long and 3 feet wide. How can she use a measuring tape to make
© 2011 Carnegie Learning
sure that the corners of the frame will be right angles?
546 • Chapter 6 Skills Practice
Lesson 6.2 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ 9. Firefighters need to cross from the roof of a 25-feet-tall building to the roof of a 35-feet-tall building by using a ladder. The buildings are 20 feet apart. What minimum length does the ladder need to be in order to span the two buildings?
Ladder
35 ft
25 ft
© 2011 Carnegie Learning
20 ft
Chapter 6 Skills Practice • 547
Lesson 6.2 Skills Practice
page 6
10. Chen is building a ramp for his remote control car. He wants the end of the ramp to extend 4 feet from the base of the ramp. The base of the ramp is 18 inches high. How long should the piece of wood for the ramp be? Round your answer to the nearest tenth.
18 in.
© 2011 Carnegie Learning
4 ft
548 • Chapter 6 Skills Practice
Lesson 6.2 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ 11. Perry wants to use a 12-foot ladder to reach a shelf that is 11 feet above the ground. How far from the wall should Perry place the base of the ladder so that the top of the ladder reaches the shelf? Round your answer to the nearest tenth.
12. Lea walks to soccer practice on Saturday. She leaves her home and walks 6 blocks north. Lea then turns east and walks 4 blocks to the soccer field. How far is the soccer field from Lea’s home?
© 2011 Carnegie Learning
Round your answer to the nearest whole number.
Chapter 6 Skills Practice • 549
Lesson 6.2 Skills Practice
page 8
Calculate the length of the segment that connects the points in each. Write your answer as a radical if necessary. 14.
13.
4 3
2 1 b2 5 c2 a 321 42 5 c2 9 1 16 5 c2
25 5 c2 ___
√25 5 c 55c
© 2011 Carnegie Learning
550 • Chapter 6 Skills Practice
Lesson 6.2 Skills Practice
page 9
Name_________________________________________________________ Date__________________________ 16.
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15.
Chapter 6 Skills Practice • 551
Lesson 6.2 Skills Practice
18.
© 2011 Carnegie Learning
17.
page 10
552 • Chapter 6 Skills Practice
Lesson 6.3 Skills Practice Name_________________________________________________________ Date__________________________
Pythagoras to the Rescue Solving for Unknown Lengths
Problem Set Determine the length of the hypotenuse of each given triangle. 2.
1.
6
c
10
c
6
24
c2 5 102 1 242 c2 5 100 1 576 c2 5 676 ____
c 5 √ 676 c 5 26
© 2011 Carnegie Learning
The length of the hypotenuse is 26 units.
Chapter 6 Skills Practice • 553
Lesson 6.3 Skills Practice
3.
page 2
4. 4
c
c
7
© 2011 Carnegie Learning
7.5
4
554 • Chapter 6 Skills Practice
Lesson 6.3 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 5.
20 4.5
6.
c
c
20
© 2011 Carnegie Learning
20
Chapter 6 Skills Practice • 555
Lesson 6.3 Skills Practice
page 4
Determine each unknown leg length.
7.
8. 20
a
13
12 11 b
122 1 b2 5 202 144 1 b2 5 400
b2 5 400 2 144
b2 5 256 ____
b5√ 256
b 5 16
© 2011 Carnegie Learning
The length of the leg is 16 units.
556 • Chapter 6 Skills Practice
Lesson 6.3 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ 9.
10. 17
b
9
a
12
© 2011 Carnegie Learning
12
Chapter 6 Skills Practice • 557
Lesson 6.3 Skills Practice
11. 9
41
page 6
12. 55
33 b
© 2011 Carnegie Learning
a
558 • Chapter 6 Skills Practice
Lesson 6.3 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ Use the Pythagorean Theorem to determine whether each given triangle is a right triangle.
14.
13.
24
17 6
7
25 15
62 1 152 0 172 36 1 225 0 289
261 fi 289
The triangle is not a right triangle.
16.
15.
2 11
3.75 9
© 2011 Carnegie Learning
4.25 8
Chapter 6 Skills Practice • 559
Lesson 6.3 Skills Practice
17.
page 8
18.
21
35
5
28
26
© 2011 Carnegie Learning
28
560 • Chapter 6 Skills Practice
Lesson 6.3 Skills Practice
page 9
Name_________________________________________________________ Date__________________________ Use the Pythagorean Theorem to calculate each unknown length. 19. The design for a bridge truss is shown. The distance between the horizontal beams is 24 feet. The distance between the vertical beams is 18 feet. Determine the length (x) of each diagonal brace. 18 ft
24 ft
x
182 1 242 5 x2 324 1 576 5 x2
900 5 x2 ____
√900 5 x
30 5 x
© 2011 Carnegie Learning
Each diagonal brace is 30 feet long.
Chapter 6 Skills Practice • 561
Lesson 6.3 Skills Practice
page 10
20. The Archery Team is practicing on the basketball court in the gymnasium. The court is 50 feet wide and 94 feet long. The archers are shooting at a target placed at one corner of the court while they
© 2011 Carnegie Learning
stand in the corner diagonally across the court. Determine the distance of each practice shot.
562 • Chapter 6 Skills Practice
Lesson 6.3 Skills Practice
page 11
Name_________________________________________________________ Date__________________________ 21. The water company installed a 40-yard diagonal brace on a water tower between two vertical beams that are 12 yards apart as shown. Determine the height of each vertical beam.
40 yd
© 2011 Carnegie Learning
12 yd
Chapter 6 Skills Practice • 563
Lesson 6.3 Skills Practice
page 12
22. The lengths of the legs of a right triangle are 15 meters each. Determine the length of the hypotenuse.
23. The length of the hypotenuse of a right triangle is 50 inches. Determine the length of the legs if
© 2011 Carnegie Learning
each leg is the same length.
564 • Chapter 6 Skills Practice
Lesson 6.3 Skills Practice
page 13
Name_________________________________________________________ Date__________________________ 24. A rescue boat leaves Walker Dock and travels 18 miles due north to haul in a sailing vessel stranded in the middle of a lake. After attaching a cable, the rescue boat hauls the sailing vessel 80 miles due east to Blue Haven Dock. Determine the direct distance from Walker Dock to Blue
© 2011 Carnegie Learning
Haven Dock.
Chapter 6 Skills Practice • 565
© 2011 Carnegie Learning
566 • Chapter 6 Skills Practice
Lesson 6.4 Skills Practice Name_________________________________________________________ Date__________________________
Meeting Friends The Distance Between Two Points in a Coordinate System
Problem Set Determine the distance between each given pair of points by graphing and connecting the points, creating a right triangle, and applying the Pythagorean Theorem. 1. (2, 2) and (8, 5) c2 5 a2 1 b2
y 8
c2 5 62 1 32
6
c2 5 36 1 9
4 2 x –8
–6
–4
–2
2 –2 –4 –6
6
8
___
c 5 √45 c < 6.71 The distance between (2, 2) and (8, 5) is approximately 6.71 units.
© 2011 Carnegie Learning
–8
4
c2 5 45
Chapter 6 Skills Practice • 567
Lesson 6.4 Skills Practice
page 2
2. (3, 7) and (7, 3) y 8 6 4 2 x –8
–6
–4
–2
2
4
6
8
–2 –4 –6 –8
3. (26, 8) and (6, 3) y 8 6
2 x –8
–6
–4
–2
2 –2 –4 –6 –8
568 • Chapter 6 Skills Practice
4
6
8
© 2011 Carnegie Learning
4
Lesson 6.4 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 4. (7, 5) and (3, 23) y 8 6 4 2 x –8
–6
–4
–2
2
4
6
8
–2 –4 –6 –8
5. (24, 24) and (5, 8) y 8 6
© 2011 Carnegie Learning
4 2 x –8
–6
–4
–2
2
4
6
8
–2 –4 –6 –8
Chapter 6 Skills Practice • 569
Lesson 6.4 Skills Practice
page 4
6. (29, 3) and (7, 5) y 8 6 4 2 x –8
–6
–4
–2
2
4
6
8
–2 –4 –6 –8
7. (27, 3) and (8, 25) y 8
4 2 x –8
–6
–4
–2
2 –2 –4 –6 –8
570 • Chapter 6 Skills Practice
4
6
8
© 2011 Carnegie Learning
6
Lesson 6.4 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ 8. (29, 6) and (8, 1) y 8 6 4 2 x –8
–6
–4
–2
2
4
6
8
–2 –4 –6 –8
Archaeologists map each item they find at a dig on a 1-foot by 1-foot coordinate grid. Calculate the distance between the given pair of objects on the coordinate grid. 9. Determine the distance between the spindle and the beads. y
c2 5 a2 1 b2
9
c2 5 42 1 32
© 2011 Carnegie Learning
8 7
c2 5 16 1 9
6 spindle
5
c2 5 25 ___
4
c 5 √25
3
c 5 5
2 1 0
The distance between the spindle and
beads 0
1
2
3
4
5
x 6
7
8
the beads is 5 feet.
9
Chapter 6 Skills Practice • 571
7721B_C3_Skills_CH06_533-610.indd 571
6/14/11 11:12 AM
Lesson 6.4 Skills Practice
page 6
10. Determine the distance between the pottery shard and the axe head. y 9 axe head
8 7 6 5 4 3 2
pottery shard
1 0
x 0
1
2
3
4
5
6
7
8
9
11. Determine the distance between the coins and the beads. y 9 8 7 6 © 2011 Carnegie Learning
coins
5 4 3 2 1 0
beads 0
1
2
3
4
5
x 6
572 • Chapter 6 Skills Practice
7
8
9
Lesson 6.4 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ 12. Determine the distance between the coins and the axe head. y 9 axe head
8 7 6 5
coins
4 3 2 1 0
x 0
1
2
3
4
5
6
7
8
9
13. Determine the distance between the mask and the beads. y 9
mask
© 2011 Carnegie Learning
8 7 6 5 4 3 2 1 0
beads 0
1
2
3
4
5
x 6
7
8
9
Chapter 6 Skills Practice • 573
Lesson 6.4 Skills Practice
page 8
14. Determine the distance between the pottery shard and the beads. y 9 8 7 6 5 4 3 pottery shard
2 1 0
beads 0
1
2
3
4
5
x 6
7
8
9
15. Determine the distance between the spindle and the axe head. y 9 axe head
8
© 2011 Carnegie Learning
7 6 5
spindle
4 3 2 1 0
x 0
1
2
3
4
5
6
574 • Chapter 6 Skills Practice
7
8
9
Lesson 6.4 Skills Practice
page 9
Name_________________________________________________________ Date__________________________ 16. Determine the distance between the mask and the coins. y 9
mask
8 7 6 5
coins
4 3 2 1 x 0
1
2
3
4
5
6
7
8
9
© 2011 Carnegie Learning
0
Chapter 6 Skills Practice • 575
© 2011 Carnegie Learning
576 • Chapter 6 Skills Practice
Lesson 6.5 Skills Practice Name_________________________________________________________ Date__________________________
Diagonally Diagonals in Two Dimensions
Problem Set Determine the length of the diagonals in each given quadrilateral. 1. The quadrilateral is a square. A
B
c2 5 a2 1 b2 c2 5 152 1 152
15 ft
c2 5 225 1 225 c2 5 450
D
C
____
c 5 √450 c < 21.21 The length of diagonal AC is approximately 21.21 feet. The length of diagonal
© 2011 Carnegie Learning
BD is approximately 21.21 feet.
Chapter 6 Skills Practice • 577
Lesson 6.5 Skills Practice
page 2
2. The quadrilateral is a rectangle. E
F
10 in.
18 in.
G
© 2011 Carnegie Learning
H
578 • Chapter 6 Skills Practice
Lesson 6.5 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 3. The quadrilateral is a parallelogram. 11 m J
K
6m
8m
M
© 2011 Carnegie Learning
N
Chapter 6 Skills Practice • 579
Lesson 6.5 Skills Practice
page 4
4. The quadrilateral is a trapezoid. y 9 8 P
7
Q
6 5 4 3
S
R
2 1 x 0
1
2
3
4
5
6
7
8
9
© 2011 Carnegie Learning
0
580 • Chapter 6 Skills Practice
Lesson 6.5 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ 5. The quadrilateral is an isosceles trapezoid. y 9 8 X
W
7 6 5 4 3 2
Y
Z
1 x 0
1
2
3
4
5
6
7
8
9
© 2011 Carnegie Learning
0
Chapter 6 Skills Practice • 581
Lesson 6.5 Skills Practice
page 6
6. The quadrilateral is a rhombus. y 9 8 G
B
7 6 5 4 3
K
M
2 1 x 0
1
2
3
4
5
6
7
8
9
© 2011 Carnegie Learning
0
582 • Chapter 6 Skills Practice
Lesson 6.5 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ Calculate the area of each shaded region. 7. The figure is composed of a circle and a rectangle. The diagonal of the rectangle is the same length as the diameter of the circle. The area of the rectangle is: 4 in.
A 5 bh A 5 (4)(9) 9 in.
A 5 36 in.2 The length of the rectangle’s diagonal is: c2 5 a2 1 b2 c2 5 42 1 92 c2 5 16 1 81 c2 5 97 ___
c 5 √ 97
© 2011 Carnegie Learning
c < 9.85 in. The area of the circle is: A 5 πr2 A < (3.14)(4.93)2 A < 76.32 in.2 The area of the shaded region is approximately 76.32 2 36 5 40.32 in.2.
Chapter 6 Skills Practice • 583
Lesson 6.5 Skills Practice
page 8
8. The figure is composed of two squares. The length of the diagonal of the smaller square is equal to the width of the larger square.
© 2011 Carnegie Learning
10 ft
584 • Chapter 6 Skills Practice
Lesson 6.5 Skills Practice
page 9
Name_________________________________________________________ Date__________________________ 9. The figure is composed of a right triangle and a circle. The hypotenuse of the right triangle is the same length as the diameter of the circle.
5m
© 2011 Carnegie Learning
12 m
Chapter 6 Skills Practice • 585
Lesson 6.5 Skills Practice
page 10
10. The figure is composed of a right triangle and a square. The hypotenuse of the right triangle is one side of the square.
15 yd
© 2011 Carnegie Learning
20 yd
586 • Chapter 6 Skills Practice
Lesson 6.5 Skills Practice
page 11
Name_________________________________________________________ Date__________________________ 11. The figure is composed of a right triangle and a semi-circle. The hypotenuse of the right triangle is the same length as the diameter of the semi-circle.
5 ft
© 2011 Carnegie Learning
5 ft
Chapter 6 Skills Practice • 587
Lesson 6.5 Skills Practice
page 12
12. The figure is composed of two right triangles. The hypotenuse of one right triangle is the leg of the other right triangle.
3 cm
4 cm
© 2011 Carnegie Learning
3 cm
588 • Chapter 6 Skills Practice
Lesson 6.6 Skills Practice Name_________________________________________________________ Date__________________________
Two Dimensions Meet Three Dimensions Diagonals in Three Dimensions
Problem Set Draw all of the edges you cannot see in each rectangular solid using dotted lines. Then draw a three-dimensional diagonal using a solid line. 2.
3.
4.
© 2011 Carnegie Learning
1.
Chapter 6 Skills Practice • 589
Lesson 6.6 Skills Practice
6.
© 2011 Carnegie Learning
5.
page 2
590 • Chapter 6 Skills Practice
Lesson 6.6 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ Determine the length of the three-dimensional diagonal in the given rectangular solid using each Pythagorean Theorem. 7. 5m
8m 8m
Length of second leg:
Length of diagonal:
c2 5 82 1 82
d2 < 11.312 1 52
c2 5 64 1 64
d2 < 127.92 1 25
c2 5 128
d2 < 152.92
____
_______
c5√ 128
d<√ 152.92
c < 11.31
d < 12.37
The length of the three-dimensional diagonal in the rectangular solid is approximately
© 2011 Carnegie Learning
12.37 meters.
Chapter 6 Skills Practice • 591
Lesson 6.6 Skills Practice
page 4
8.
10 in.
1 in.
© 2011 Carnegie Learning
4 in.
592 • Chapter 6 Skills Practice
Lesson 6.6 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ 9.
11 cm 6 cm
© 2011 Carnegie Learning
3 cm
Chapter 6 Skills Practice • 593
Lesson 6.6 Skills Practice
page 6
10.
15 m
3m
© 2011 Carnegie Learning
4m
594 • Chapter 6 Skills Practice
Lesson 6.6 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ 11.
9 ft
5 ft
© 2011 Carnegie Learning
12 ft
Chapter 6 Skills Practice • 595
Lesson 6.6 Skills Practice
page 8
12.
14 in.
13 in.
© 2011 Carnegie Learning
7 in.
596 • Chapter 6 Skills Practice
Lesson 6.6 Skills Practice
page 9
Name_________________________________________________________ Date__________________________ Use the diagonals across the front face, the side face, and the top face of each given solid to determine the length of the three-dimensional diagonal. Use a formula. 13.
3"
6"
8"
d2 5 __ 1 (32 1 62 1 82) 2 d2 5 __ 1 (9 1 36 1 64) 2 1 (109) d2 5 __ 2 d2 5 54.50 ______
d5√ 54.50 d < 7.38
© 2011 Carnegie Learning
The length of the three-dimensional diagonal is approximately 7.38 inches.
Chapter 6 Skills Practice • 597
Lesson 6.6 Skills Practice
14.
page 10
9m 3m
© 2011 Carnegie Learning
10 m
598 • Chapter 6 Skills Practice
Lesson 6.6 Skills Practice
page 11
Name_________________________________________________________ Date__________________________ 15.
8 ft
12 ft
© 2011 Carnegie Learning
10 ft
Chapter 6 Skills Practice • 599
Lesson 6.6 Skills Practice
16.
page 12
6m
6m
© 2011 Carnegie Learning
5m
600 • Chapter 6 Skills Practice
Lesson 6.6 Skills Practice
page 13
Name_________________________________________________________ Date__________________________ 17.
8 yd
10 yd
© 2011 Carnegie Learning
4 yd
Chapter 6 Skills Practice • 601
Lesson 6.6 Skills Practice
18.
page 14
3"
13"
© 2011 Carnegie Learning
15"
602 • Chapter 6 Skills Practice
Lesson 6.6 Skills Practice
page 15
Name_________________________________________________________ Date__________________________ Use a formula to answer each question. 19. A packing company is in the planning stages of creating a box that includes a three-dimensional diagonal support inside the box. The box has a width of 5 feet, a length of 6 feet, and a height of 8 feet. How long will the diagonal support need to be? d2 5 52 1 62 1 82 d2 5 25 1 36 1 64 d2 5 125 ____
d5√ 125 d < 11.18 The diagonal support will need to be approximately 11.18 feet.
20. A plumber needs to transport a 12-foot pipe to a jobsite. The interior of his van is 90 inches in
© 2011 Carnegie Learning
length, 40 inches in width, and 40 inches in height. Will the pipe fit inside his van?
Chapter 6 Skills Practice • 603
Lesson 6.6 Skills Practice
page 16
21. You are landscaping the flower beds in your front yard. You choose to plant a tree that measures 5 feet from the root ball to the top. The interior of your car is 60 inches in length, 45 inches in width, and 40 inches in height. Will the tree fit inside your car?
22. Julian is constructing a box for actors to stand on during a school play. To make the box stronger he decides to include diagonals on all sides of the box and a three-dimensional diagonal through the center of the box. The diagonals across the front and back of the box are each 2 feet, the diagonals across the sides of the box are each 3 feet, and the diagonals across the top and
© 2011 Carnegie Learning
bottom of the box are each 7 feet. How long is the diagonal through the center of the box?
604 • Chapter 6 Skills Practice
Lesson 6.6 Skills Practice
page 17
Name_________________________________________________________ Date__________________________ 23. Carmen has a cardboard box. The length of the diagonal across the front of the box is 9 inches. The length of the diagonal across the side of the box is 7 inches. The length of the diagonal across the top of the box is 5 inches. Carmen wants to place a 10-inch stick into the box and be able to
© 2011 Carnegie Learning
close the lid. Will the stick fit inside the box?
Chapter 6 Skills Practice • 605
Lesson 6.6 Skills Practice
page 18
24. A technician needs to pack a television in a cardboard box. The length of the diagonal across the front of the box is 17 inches. The length of the diagonal across the side of the box is 19 inches. The length of the diagonal across the top of the box is 20 inches. The three-dimensional diagonal of the television is 24 inches. Will the television fit in the box?
Determine each unknown measurement. 25. A rectangular box has a length of 8 inches and a width of 5 inches. The length of the threedimensional diagonal of the box is 12 inches. What is the height of the box?
122 5 82 1 52 1 h2 144 5 64 1 25 1 h2 55 5 h2 ___
√55 5 h 7.42 < h The height of the box is approximately 7.42 inches.
606 • Chapter 6 Skills Practice
© 2011 Carnegie Learning
d2 5 l2 1 w2 1 h2
Lesson 6.6 Skills Practice
page 19
Name_________________________________________________________ Date__________________________ 26. The length of the diagonal across the front of a rectangular box is 6 feet, and the length of the diagonal across the top of the box is 9 feet. The length of the three-dimensional diagonal is 14 feet. What is the length of the diagonal across the side of the box?
27. A rectangular box has a length of 7 feet and a height of 11 feet. The length of the
© 2011 Carnegie Learning
three-dimensional diagonal of the box is 20 feet. What is the width of the box?
Chapter 6 Skills Practice • 607
Lesson 6.6 Skills Practice
page 20
28. The length of the diagonal across the side of a rectangular box is 16 centimeters, and the length of the diagonal across the top of the box is 18 centimeters. The length of the three-dimensional diagonal is 20 centimeters. What is the length of the diagonal across the front of the box?
29. A rectangular box has a height of 3 feet and a width of 4 feet. The length of the three-dimensional
© 2011 Carnegie Learning
diagonal of the box is 13 feet. What is the length of the box?
608 • Chapter 6 Skills Practice
Lesson 6.6 Skills Practice
page 21
Name_________________________________________________________ Date__________________________ 30. The length of the diagonal across the front of a rectangular box is 30 inches, and the length of the diagonal across the side of the box is 30 inches. The length of the three-dimensional diagonal is
© 2011 Carnegie Learning
40 inches. What is the length of the diagonal across the top of the box?
Chapter 6 Skills Practice • 609
© 2011 Carnegie Learning
610 • Chapter 6 Skills Practice
