Pythagorean Theorem Practice Problems with Answers

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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