Lesson 7-4: Converse of the Pythagorean Theorem — Practice Questions

1. 1. Which of the following sets of numbers is a Pythagorean triple?

   • A. (8, 15, 17)
   • B. (8, 15, 16)
   • C. (7, 15, 17)
   • D. (8, 14, 17)

2. 2. A right triangle has legs measuring 21 cm and 28 cm. If the side lengths form a Pythagorean triple, what is the length of the hypotenuse in cm? ___

3. 3. The side lengths of four triangles are given below. Which set of lengths forms a right triangle?

   • A. 10, 24, 26
   • B. 10, 24, 25
   • C. 5, 12, 14
   • D. 10, 22, 26

4. 4. The legs of a right triangle measure 14 inches and 48 inches. The side lengths form a Pythagorean triple. What is the length of the hypotenuse in inches? ___

5. 5. True or False: A triangle with side lengths of 20, 48, and 52 is a right triangle.

   • A. True
   • B. False

6. 6. A right triangle has legs of length 16 and 30. Using a Pythagorean triple, what is the length of the hypotenuse? ___

7. 7. Which of the following sets of side lengths forms a right triangle?

   • A. 15, 36, 38
   • B. 21, 72, 75
   • C. 8, 15, 18
   • D. 9, 12, 14

8. 8. A right triangle has a hypotenuse of length 39 and one leg of length 36. What is the length of the other leg? ___

9. 9. If the numbers $a, b, c$ form a Pythagorean triple, which of the following sets is also guaranteed to be a Pythagorean triple for any positive integer $k$?

   • A. $a+k, b+k, c+k$
   • B. $ak, bk, ck$
   • C. $a^2, b^2, c^2$
   • D. $\sqrt{a}, \sqrt{b}, \sqrt{c}$

10. 10. The lengths of two sides of a right triangle are 30 and 50. If 50 is the hypotenuse, what is the length of the other leg? ___