# Pythagorean Triangle/Examples/7-24-25

## Example of Primitive Pythagorean Triangle

The triangle whose sides are of length $7$, $24$ and $25$ is a primitive Pythagorean triangle.

## Proof

 $\ds 7^2 + 24^2$ $=$ $\ds 49 + 576$ $\ds$ $=$ $\ds 625$ $\ds$ $=$ $\ds 25^2$

It follows by Pythagoras's Theorem that $7$, $24$ and $25$ form a Pythagorean triple.

Note that $7$ and $24$ are coprime.

Hence, by definition, $7$, $24$ and $25$ form a primitive Pythagorean triple.

The result follows by definition of a primitive Pythagorean triangle.

$\blacksquare$