9-5 The Pythagorean Theorem
Name
Date
A diagonal fence creates two triangular fields. Each field has a height
of 240 ft and a base of 380 ft. What is the length of the diagonal fence?
Write the answer in simplest radical form.
a2 ⫹ b2 ⫽ c2
2402 ⫹ 3802 ⫽ c2
240 ft
Use the Pythagorean Theorem.
Substitute values into the Pythagorean Theorem.
380 ft
57,600 ⫹ 144,400 ⫽ c2
Simplify.
202,000 ⫽ c2
Simplify.
202 ,000 ⫽ c
Take the square root of both sides.
20 505 ⫽ c
Write in simplest radical form:
202 ,000 ⫽
400 • 505
The length of the diagonal fence is 20 505 feet.
Find the length of the third side of each right triangle. Give your
answer in simplest radical form.
2.
1.
3.
7
?
18
24
3
?
?
24
Copyright © by William H. Sadlier, Inc. All rights reserved.
10
a2 b 2 c 2
242 182 c 2
576 324 c 2
900 c 2
900 c
c 30
4.
5.
6
32 72 c2
9 49 c2
58 c2
c 58
242 102 c2
576 100 c2
676 c2
c 26
6.
9
13
5
?
?
?
5
3
52 62 c2
25 36 c2
61 c2
c 61
a2 32 132
a2 9 169
a2 160
a 16 • 10
a 4 10
Lesson 9-5, pages 236–237.
a2 52 92
a2 25 81
a2 56
a 4 • 14
a 2 14
Chapter 9
229
For More Practice Go To:
Determine whether or not a right triangle can have sides of the
given lengths.
8. 5, 5, 7
a2 b2 c2
?
12 12 52
?
1 1 25
2 25 False
10. 3, 6 2 , 9
?
?
?
no
?
3 1
?
yes
14. 3 , 3 , 2
25 1 ?
4
9
9
26
4 False
9
1 ?
9
1
16 16
10
1 False
16
no
no
15. Bill traveled due north for 5 miles, then
7 miles due west, and then 74 miles
southeast towards his starting point. Did Bill
arrive at his starting point? Explain how
you know.
?
5 1
13. 4 , 4 , 1
4.52 62 7.52
?
20.25 36 56.25
56.25 56.25 True
yes
yes
yes
12. 4.5, 6, 7.5
3.62 4.82 62
?
12.96 23.04 36
36 36 True
32 (6 2 )2 92
?
9 72 81
81 81 True
22 (4 2 )2 62
?
4 32 36
36 36 True
52 52 72
50 49 False
no
11. 3.6, 4.8, 6
9. 2, 4 2 , 6
16. The side of a square is 9 inches. What is the
length of each diagonal?
?
Make a drawing; 52 72 ( 74 )2; 25 49 74
74 74 True. Bill traveled following the shape
of a right triangle. To arrive at his starting point,
52 72 would have to equal 74. Because it does,
Bill arrived at the same place where he began.
17. What is the length of the unknown side of
the figure?
Make a drawing of a square with sides of 9 in.
Then draw a diagonal with length of c; 92 92 c2
81 81 c2; 162 c2; 162 c; 9 2 c
The length of each diagonal is 9 2 in.
18. What is the perimeter of the square?
4
5
10
?
8
Reason logically using the Pythagorean
Theorem twice: 82 a2 102
64 a2 100; a2 36; a 6
62 42 c2; 36 16 c2; 52 c2; 2 13 c
The length of the unknown side of the figure
is 2 13.
19. ( 15 ⫹ 12)( 15 ⫺ 12)
15 144
129
230
Chapter 9
Reason logically using the Pythagorean Theorem.
a2 a2 52; 2a2 25
25
a2 ; a 25 ; a 5 2
2
2
2
5
2
P4•
10 2
2
The perimeter of the square is 10 2 units.
20. ( 21 ⫹ 16)( 17 ⫺ 17 )
0
Copyright © by William H. Sadlier, Inc. All rights reserved.
7. 1, 1, 5