Question

A triangle has sides with lengths of 8 meters, 15 meters, and 17 meters. Is it a right triangle?

Answer 1

A Right Triangle must satisfy the Converse of the Pythagorean Theorem:
`a^2 + b^2 = c^2`

From the given side lengths, let a = 8, b = 15, c = 17 (c cannot be less than a or b)

`a^2 + b^2 = (8)^2 + (15)^2`

`a^2 + b^2 = 64 + 225 = 289`

`c^2 = (17)^2 = 289`

`a^2 + b^2 = c^2 \ (289 = 289)`

Therefore, a Triangle with side lengths of 8, 15 and 17 is a Right Triangle

Note: Since the side lengths are positive integers and the GCF(8, 15, 17) = 1, they are a primitive Pythagorean Triple.