Determine whether a Triangle with side lengths of 39, 80 and 89 is a Right Triangle

A Right Triangle must satisfy the Converse of the Pythagorean Theorem: a² + b² = c²
From the given side lengths, let a = 39, b = 80, c = 89  (c cannot be less than a or b)
a² + b² = (39)² + (80)²
a² + b² = 1,521 + 6,400 = 7,921
c² = (89)² = 7,921
a² + b² = c²  (7,921 = 7,921)
Therefore, a Triangle with side lengths of 39, 80 and 89 is a Right Triangle
Note: Since the side lengths are positive integers and the GCF(39, 80, 89) = 1, they are a primitive Pythagorean Triple