exponents and polynomials using the pythagorean theorem

Question

the longer leg of a right triangle is 7 cm longer than the shorter leg. the hypotenuse is 9 cm longer than the shorter leg. find the sides lengths of the triangle.

Answer 1

Let X = length of shorter leg, cm

X + 7 = length of longer leg, cm

X + 9 = length of hypotenuse, cm

X^2 + (X + 7)^2 = (X + 9)^2

X^2 + X^2 + 14X+ 49 = x^2 + 18X + 81

X^2 - 4X - 32 = 0

(X - 8)(X + 4) = 0

X = 8 and X = -4

The negative answer is rejected and we take X = 8 cm for the shorter leg.

X = 8 + 7 = 15 cm for the longer leg.

X = 8 + 9 = 17 cm for the hypotenuse.