Pythagorean Theorem Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Pythagorean Theorem.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
If you draw squares on each side of a right triangle, the two smaller squares fill the big one exactly.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: A fundamental relationship between sides of right triangles.
Common stuck point: c must be the longest side (hypotenuse), opposite the right angle.
Sense of Study hint: Ask yourself: which side is across from the 90-degree angle? Label that one c, then plug the other two into a-squared plus b-squared.
Worked Examples
Example 1
easySolution
- 1 Apply the Pythagorean theorem: a^2 + b^2 = c^2.
- 2 Substitute: 3^2 + 4^2 = c^2 \Rightarrow 9 + 16 = c^2 \Rightarrow c^2 = 25.
- 3 Take the positive square root: c = \sqrt{25} = 5.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
hardExample 2
hardBackground Knowledge
These ideas may be useful before you work through the harder examples.