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The Pythagorean Theorem Practice Questions

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Updated on Oct 1, 2011

Read the following study guide for a concept review:

The Pythagorean Theorem Study Guide

Practice Questions

Find the length of the side labeled x in each triangle.

1. The Pythagorean Theorem
2. The Pythagorean Theorem
3. The Pythagorean Theorem
4. The Pythagorean Theorem
5. The Pythagorean Theorem
6. The Pythagorean Theorem
7. The Pythagorean Theorem
8. The Pythagorean Theorem
9. Find the hypotenuse of a right triangle with legs 2 feet and 7 feet long.
10. If a right triangle has a hypotenuse length of 10 feet and one leg length of 5 feet, what is the length of the other leg?
11. Suppose the hypotenuse of a right triangle is 50 cm long, and another side is 30 cm long. What is the length of the third side?
12. A right triangle has a one-meter leg and a two-meter leg. How long is the hypotenuse?
13. The diagonal (hypotenuse) of a large right triangle is 6 miles long. If one leg is 2 miles long, how long is the other leg?
14. What is the hypotenuse of a right triangle with both legs 6 inches in length?
15. What is the hypotenuse of a right triangle with both legs 10 inches in length?
16. Suppose a right triangle has a leg length of 1.2 meters and a hypotenuse length of 3.6 meters. What is the length of the third side?
17. The hypotenuse of a right triangle is 30 inches long. If one leg measures 9.1 inches, what is the length of the other leg?
18. What is the hypotenuse of a right triangle with legs feet and feet long?
19. How long is the diagonal of a standard piece of paper that measures by 11 inches?
20. A 20-foot ladder must always be placed 5 feet from a wall it is leaned against. What is the highest spot on a wall that the ladder can reach?
21. Televisions and computer screens are always measured on the diagonal. If a 14-inch computer screen is 12 inches wide, how tall is the screen?
22. The bottom of a cardboard box is a 20-inch square. What is the widest object that could be wedged in diagonally?

 

Which of the following are Pythagorean triples?

23. 20-21-29
24. 15-30-34
25. 12-60-61
26. 12-35-37
27. 33-56-65

 

Find the Pythagorean triple generated by the given r and s.

28. r = 4 and s = 1
29. r = 3 and s = 2
30. r = 9 and s = 4
31. r = 5 and s = 3
32. r = 10 and s = 3
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