Pythagorean Triangle/Examples/3-4-5

Example of Primitive Pythagorean Triangle
The triangle whose sides are of length $3$, $4$ and $5$ is a primitive Pythagorean triangle.


 * 3-4-5.png

Proof
It follows by Pythagoras's Theorem that $3$, $4$ and $5$ form a Pythagorean triple.

Note that $3$ and $4$ are coprime.

Hence, by definition, $3$, $4$ and $5$ form a primitive Pythagorean triple.

The result follows by definition of a primitive Pythagorean triangle.

Also see

 * Smallest Pythagorean Triangle is 3-4-5
 * Pythagorean Triangle whose Area is Half Perimeter: its area and semiperimeter are both $6$
 * Pythagorean Triangle with Sides in Arithmetic Progression