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.