TOPICS
Search

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

 r=1/2(a+b-c).

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

 A=1/2ab

is always a positive integer.


See also

Primitive Right Triangle, Pythagorean Triple, Right Triangle

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Pythagorean Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PythagoreanTriangle.html

Subject classifications