Pythagorean Triangle

A Pythagorean triangle is a right triangle with integer side lengths (i.e., whose side lengths (a,b,c) form a Pythagorean triple). A Pythagorean triangle with GCD(a,b,c)=1 is known as a primitive right triangle.

The inradius r 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 a or b must be even, and for imprimitive triples, both a and b are even, so


is always a positive integer.

See also

Primitive Right Triangle, Pythagorean Triple, Right Triangle

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Cite this as:

Weisstein, Eric W. "Pythagorean Triangle." From MathWorld--A Wolfram Web Resource.

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