algebra question

Question

Incline mats, or triangle mats, are offered with different levels of incline to help gymnasts learn basic moves. As the name may suggest, two sides of the mat are right triangles. If the height of the mat is 14 inches shorter than the length of the mat and the hypotenuse is 4 inches longer than the length of the mat, what is the length of the mat?

Answer 1

Let a = the length of the mat.

a² + (a - 14)² = (a + 4)²

a² + a² - 28a + 196 = a² + 8a + 16

a² - 36a + 180 = 0

(a - 30)(a - 6) = 0

a - 30 = 0

a = 30 in

a - 6 = 0

a = 6

We have to disregard this solution since 14 inches shorter would be -8 inches.