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Pythagorean Theorem Practice Problems

Grades 7-10 · 5 problems

Practice using the Pythagorean Theorem to find missing side lengths in right triangles. This tool provides instant feedback and step-by-step solutions.

Tip: The Pythagorean Theorem only applies to right triangles. Make sure you can identify the hypotenuse (the side opposite the right angle) and the legs (the two sides that form the right angle).
1

A right triangle has legs of length 3 and 4. What is the length of the hypotenuse?

2

A right triangle has a leg of length 12 and a hypotenuse of length 13. What is the length of the other leg?

3

A ladder is leaning against a wall. The base of the ladder is 6 feet from the wall, and the ladder reaches 8 feet up the wall. How long is the ladder?

4

A right triangle has legs of length x and x, and a hypotenuse of length 10. What is the value of x?

5

Two cars start at the same point. One car travels east for 60 miles, and the other car travels north for 80 miles. How far apart are the two cars?

Common Mistakes

  • Forgetting to square the side lengths before adding them.
  • Incorrectly identifying the hypotenuse.
  • Taking the square root too early or not at all.
  • Using the Pythagorean Theorem on non-right triangles.