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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