# 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.

*Note: drawings not to scale*

**Problem 1:** Find the value of [latex]x[/latex] in the right triangle.

## Answer

[latex]10[/latex]

**Problem 2:** Find the value of [latex]x[/latex] in the right triangle.

## Answer

[latex]4\sqrt 7 [/latex]

**Problem 3:** Find the value of [latex]x[/latex] in the right triangle.

## Answer

[latex]3[/latex]

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

## Answer

[latex]13[/latex]

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

## Answer

[latex]15[/latex]

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

## Answer

[latex]\sqrt {10} [/latex]

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

## Answer

[latex]2\sqrt 6[/latex]

**Problem 8:** Find the value of [latex]x[/latex] of the right isosceles triangle.

## Answer

[latex]\sqrt 6[/latex]

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