Pythagorean Triangle

A Pythagorean triangle is a right triangle with integer side lengths (i.e., whose side lengths  form a Pythagorean triple). A Pythagorean triangle with  is known as a primitive right triangle.

The inradius  of a Pythagorean triangle is always a whole number since

The area of such a triangle is also a whole number since for primitive Pythagorean triples, one of  or  must be even, and for imprimitive triples, both  and  are even, so

is always a positive integer.