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.