Can you explain the Pythagorean theorem with an example?

The Pythagorean theorem applies to right triangles—triangles with one 90° angle.

It says:

$$a^2+b^2=c^2$$

• $a$ and $b$ are the two shorter sides.
• $c$ is the hypotenuse, the longest side opposite the right angle.

Example

Suppose the shorter sides measure 3 cm and 4 cm:

$$3^2+4^2=c^2$$ $$9+16=c^2$$ $$25=c^2$$

Take the square root:

$$c=5$$

So the hypotenuse is 5 cm. This is known as a 3–4–5 right triangle.