Pythagorean Theorem Practice Problems with Answers

There are eight (8) problems here about the Pythagorean Theorem for you to work on. When you do something a lot, you get better at it. Let’s get started!

Here’s the Pythagorean Theorem formula for your quick reference.

Pythagorean Theorem - a squared plus b squared is equal to c squared

Note: drawings not to scale


Problem 1: Find the value of x in the right triangle.

the legs of a right triangle are 6 and 8
Answer

10


Problem 2: Find the value of x in the right triangle.

the leg of a right triangle is 12 and the hypotenuse is 16
Answer

4\sqrt 7


Problem 3: Find the value of x in the right triangle.

right triangle with legs square root 3 and square root 6
Answer

3


Problem 4: The legs of a right triangle are 5 and 12. What is the length of the hypotenuse?

Answer

13


Problem 5: The leg of a right triangle is 8 and its hypotenuse is 17. What is the measure of its other leg?

Answer

15


Problem 6: Suppose the shorter leg of a right triangle is \sqrt 2. The longer leg is twice the shorter leg. Find the hypotenuse.

Answer

\sqrt {10}


Problem 7: The hypotenuse of a right triangle is 4\sqrt 2. If the longest leg is half the hypotenuse, what is the length of the shortest leg?

Answer

2\sqrt 6


Problem 8: Find the value of x of the right isosceles triangle.

the hypotenuse of a right isosceles triangle is 2 times square root 3
Answer

\sqrt 6


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