Pythagorean Theorem Quiz
15 questions · free · new questions every attempt · Updated September 26, 2026
The Pythagorean theorem links the three sides of a right triangle: a² + b² = c². It is used for ladders, screen sizes, map distances and more. In this quiz you find hypotenuses, missing legs and distances between points, using numbers that give whole-number answers.
What this quiz covers
- Finding the hypotenuse given two legs
- Finding a missing leg given the hypotenuse
- Recognising common Pythagorean triples
- Using the distance formula on a grid
- Square roots of perfect squares
- Checking that the hypotenuse is the longest side
How to prepare
Learn 3-4-5, 5-12-13, 8-15-17 and their multiples, and you will spot many answers instantly. Always square first, add or subtract, then take the square root. Check that your hypotenuse is longer than both legs. See the theorem guide for the visual proof.
Sample questions with answers
These five questions show the style. Your quiz above will have different numbers each time.
- A right triangle has legs 9 and 12. What is the length of the hypotenuse?
Show answer
15. c² = 9² + 12² = 225, so c = 15.
- A right triangle has hypotenuse 15 and one leg 9. What is the other leg?
Show answer
12. b² = 15² − 9² = 144, so b = 12.
- What is the distance between (3, 1) and (9, 9)?
Show answer
10. d = √(6² + 8²) = √100 = 10.
- A right triangle has hypotenuse 13 and one leg 5. What is the other leg?
Show answer
12. b² = 13² − 5² = 144, so b = 12.
- What is the distance between (-1, 3) and (7, 9)?
Show answer
10. d = √(8² + 6²) = √100 = 10.
Frequently asked questions
What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
What is a Pythagorean triple?
Three whole numbers that satisfy the theorem, like 3, 4 and 5.
Can I check answers with a tool?
Yes, use the Pythagorean theorem calculator.
Keep practising
The Pythagorean Theorem Explained6 min readPythagorean Theorem CalculatorFind the hypotenuse or a missing leg of a right triangle, plus area, perimeter and angles.
Multiplication Quiz15 questionsFractions Quiz15 questionsDecimals Quiz15 questionsReviewed September 26, 2026 by the SolveCalcPro editorial team. Questions are generated from tested formulas. Spot a mistake? Tell us.