Pythagorean Theorem Example

Grade 8Key Stage 3-4Årskurs 8-9

Problem

A right triangle has one leg of 5 cm and a hypotenuse of 13 cm. Find the other leg.

📝Step-by-Step Solution

Write the Pythagorean theorem

The Pythagorean theorem states: a² + b² = c², where c is the hypotenuse (longest side).

a² + b² = c²

Identify what we know

One leg a = 5, hypotenuse c = 13. We need to find leg b.

a = 5, c = 13, b = ?

Substitute into the formula

Plug in the known values: 5² + b² = 13²

5² + b² = 13²

Calculate the squares

25 + b² = 169

Isolate b²

Subtract 25 from both sides: b² = 169 - 25 = 144

b² = 144

Take the square root

b = √144 = 12

b = 12 cm

✅Final Answer

The other leg is 12 cm

This is a 5-12-13 Pythagorean triple! Common Pythagorean triples to memorize: 3-4-5, 5-12-13, 8-15-17, 7-24-25. When finding a leg (not hypotenuse), rearrange to: leg² = hypotenuse² - other leg².

Ready to Practice Pythagorean Theorem?

Generate a personalized practice test with MathQuizily. Get instant PDF downloads with answer keys.

Create Ready-to-Use Math Test (PDF)Ready in minutes. No editing needed.Open the AI math test generator

Learn more about Pythagorean Theorem

This worked example is part of the broader pythagorean theorem guide. Review the method, practice related skills, and create a printable assessment when you are ready.

Open the Pythagorean Theorem guide

📖More Pythagorean Theorem Examples

Find the Hypotenuse (3-4-5 Triangle)

A right triangle has legs of length 3 and 4. Find the length of the hypotenuse.

Easy

Back to Pythagorean Theorem Guide

Build the assessment, not just the questions

MathQuizily helps teachers move from a topic or standard to a printable math test with answer keys, balanced difficulty, and classroom-ready PDF output.

A useful assessment should make the learning target clear, cover the intended skills, and give the teacher enough information to review the result before students see it. The workflow supports short quizzes, chapter checks, diagnostic tests, homework packets, make-up assessments, and equivalent retake versions.

Choose a grade, topic, curriculum context, and difficulty level. The generated PDF includes a student version and a separate worked answer key, so teachers can print, review, and grade without reformatting questions or building solutions from scratch. No student account is required to create or print a test.