Name____________________________________________ Date________________ Class__________
7.1-2 Pythagorean Theorem Practice
Find the unknown leg length x. Write your answer in simplest radical form
1.
3.
2.
4.
Find the area of the isosceles triangle. Write your answer in simplest radical form.
5.
6.
The given lengths are two sides of a right triangle. All three side lengths of the
triangle are integers and together form a Pythagorean triple. Find the length of
the third side and tell whether it is a leg or the hypotenuse.
7. 24 and 32
8. 72 and 78
Find the area of a right triangle with given leg l and hypotenuse h. Round
decimal answers to the nearest tenth.
9. l = 13 cm, h = 19cm
10. l = 8.4 mi, h = 29 mi
Find the area of the right triangle. Write your answer in simplest radical form.
11.
12.
13. One leg of a right triangle is twice as long as the other leg. The area of the triangle is
49 square feet. What is the length of the shorter leg?
A. 5 ft
B. 6 ft
C. 7 ft
D. 8 ft
Find the unknown side length x. Write your answer in simplest radical form.
14.
15.
16.
A farmer is planning on cultivating a triangular plot of land as shown in the diagram. The
plot has an area of 12,600 square feet.
17. Find the perimeter of the plot of land.
18. One acre of land is equivalent to 43,560 square feet. How many
acres are in this plot of land? Round to two decimal places.
19. The farmer wants to enclose the land with a fence. A post will
be placed every 12 feet around the perimeter. How many posts
are needed?
Decide whether the numbers can represent the side lengths of a triangle. If they
can, classify the triangle as acute, right, or obtuse.
20. 26, 35, 62
21. 14, 18, 29
22. 30, 72, 78
23. 17, 19, 22
Graph points A, B, and C. Connect the points to form ΔABC. Decide whether ΔABC
is acute, right, or obtuse.
24. A(2, 1), B(3, 4), C(6, 5)
25. A( 2, 3), B(l, 5), C(6, 5)
Copy and complete the statement with <, >, or =.
26. m J ____ m R
27. m K + m L ____ m S + m T
The sides and classification of a triangle are given below. The length of the
longest side is the integer given. What value(s) of x make the triangle?
28. x, x, 16; right
29. x, x, 10; obtuse
30. x, x, 15; acute
31.
Many railroad bridges are designed using triangular structures like the one in the
diagram. All five triangles in the design are congruent. The length of the bridge is 48
feet and the height is 15 feet. How many feet of material are needed to build one side
of the bridge as shown in the diagram?
32.
The figure represents a rectangular storage shed and its dimensions are given in
feet. Can you fit an 18 foot 6 inch pipe in the shed?
Answer Key: Lesson 7.1&7.2
20. no
21. yes; obtuse
22. yes; obtuse
23. yes; acute
24.
1. 5 13
2. 4 73
3.
301
4. 18 2
5. 7 51 in.2
6. 375 51 ft2
7.
8.
9.
10.
11.
4
40; hypotenuse
30; leg
90.1 cm2
116.6
7 51
2
mi2
obtuse
25.
in.2
12. 48 10 m2
13. C
14. 8 2
15. 2 22
16.
17.
18.
19.
2 127
571.9 ft
0.29
48
acute
26. m J < m R
27. m K + m L > m
28. 8 2
29. 5 < x < 5 2
30. x
15 2
2
31. 182 ft
32. no
S+m
T