Given Side Lengths: 65, 63, 16
A Right Triangle must satisfy the Converse of the Pythagorean Theorem: a2 + b2 = c2
From the given side lengths, let a = 16, b = 63, c = 65 (c cannot be less than a or b)
a2 + b2 = (16)2 + (63)2
a2 + b2 = 256 + 3,969 = 4,225
c2 = (65)2 = 4,225
a2 + b2 = c2 (4,225 = 4,225)
Therefore, a Triangle with side lengths of 16, 63 and 65 is a Right Triangle
Note: Since the side lengths are positive integers and the GCF(16, 63, 65) = 1, they are a primitive Pythagorean Triple
A Right Triangle must satisfy the Converse of the Pythagorean Theorem: a2 + b2 = c2
From the given side lengths, let a = 16, b = 63, c = 65 (c cannot be less than a or b)
a2 + b2 = (16)2 + (63)2
a2 + b2 = 256 + 3,969 = 4,225
c2 = (65)2 = 4,225
a2 + b2 = c2 (4,225 = 4,225)
Therefore, a Triangle with side lengths of 16, 63 and 65 is a Right Triangle
Note: Since the side lengths are positive integers and the GCF(16, 63, 65) = 1, they are a primitive Pythagorean Triple