Pythagorean Triangle/Examples/6-8-10

Example of Pythagorean Triangle
The triangle whose sides are of length $6$, $8$ and $10$ is a Pythagorean triangle.

This is not a primitive Pythagorean triangle.


 * 6-8-10.png

Proof
It follows by Pythagoras's Theorem that $6$, $8$ and $10$ form a Pythagorean triple.

Note that $6$ and $8$ are not coprime as $\gcd \left\{ {6, 8}\right\} = 2$.

Hence, by definition, $6$, $8$ and $10$ do not form a primitive Pythagorean triple.

The result follows by definition of a primitive Pythagorean triangle.