right triangle

Question

One leg of a right triangle is 49 inches longer than the other leg, and the hypotenuse is 91 inches. Find the lengths of the legs of the triangle.

Answer 1

a² + (a + 49)² = 91²

a² + a² + 98a + 2401 = 8281

2a² + 98a - 5880 = 0

a² + 49a - 2940 = 0

(a + 84)(a - 35) = 0

 

a + 84 = 0

a = -84

We don't measure in negatives, so we disregard this answer.

 

a - 35 = 0

a = 35"

 

35 + 49 = 84"