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Pythagorean triangles whose area is twice the perimeter

Source: Dutch NMO 2003 p1

September 21, 2019
Pythagorean TripleIntegerareaperimetergeometry

Problem Statement

A Pythagorean triangle is a right triangle whose three sides are integers. The best known example is the triangle with rectangular sides 33 and 44 and hypotenuse 55. Determine all Pythagorean triangles whose area is twice the perimeter.