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 [latex]x[/latex] in the right triangle.

the legs of a right triangle are 6 and 8
Answer

[latex]10[/latex]


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

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

[latex]4\sqrt 7 [/latex]


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

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

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

[latex]\sqrt 6[/latex]


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