Solving Problems Using the Pythagorean Theorem Practice — Grade 9 math

Lesson 85: Solving Problems Using the Pythagorean Theorem — Practice Questions

1. A right triangle has legs of length 9 and 12. What is the length of the hypotenuse? ___
2. In a right triangle, the side opposite the right angle is called the hypotenuse. If the legs have lengths $x$ and $y$ and the hypotenuse has length $z$, which equation is correct?
- A. $x^2 + z^2 = y^2$
- B. $x^2 + y^2 = z^2$
- C. $x + y = z$
- D. $z^2 - x^2 = y$
3. A right triangle has a hypotenuse of length 25 and one leg of length 7. What is the length of the other leg? ___
4. A rectangular park is 15 meters long and 8 meters wide. If you walk diagonally from one corner to the opposite corner, how far do you walk?
- A. 23 meters
- B. 17 meters
- C. $\sqrt{161}$ meters
- D. 7 meters
5. A right triangle has legs with lengths 2 and 4. What is the length of the hypotenuse in simplest radical form? ___
6. Which of the following sets of side lengths forms a Pythagorean triple?
- A. 7, 24, 25
- B. 6, 8, 11
- C. 5, 10, 12
- D. 4, 5, 6
7. The two legs of a right triangle have lengths 9 and 12. The length of the hypotenuse that completes this Pythagorean triple is ___.
8. Which of the following sets of numbers is NOT a Pythagorean triple?
- A. 8, 15, 17
- B. 5, 12, 13
- C. 9, 40, 41
- D. 6, 11, 13
9. A right triangle has a leg of length 7 and a hypotenuse of length 25. The length of the other leg that forms a Pythagorean triple is ___.
10. According to the definition, which set cannot be a Pythagorean triple because one of its members is not a whole number?
- A. 10, 24, 26
- B. 2, 3, 4
- C. 9, 12, 15
- D. 5, 6, $\sqrt{61}$