Question

The longer leg of a right triangle is 4 inches longer than the shorter leg. The hypotenuse is 8 inches longer than the shorter leg. Find the side lengths of the

triangle.

Answer 1

lengths are 12, 16, and 20

Explanation:

let 's' = length of smaller leg

let '4+s' = length of second leg

let '8+s' = length of hypotenuse

Now use the Pythagorean Theorem: a² + b² = c²

s² + (4+s)² = (8+s)²

s² + 16 + 8s + s² = 64 + 16s + s²

2s² + 8s + 16 = 64 + 16s + s²

subtract s² from each side:

s² + 8s + 16 = 64 + 16s

subtract '16s' from each side:

s² - 8s + 16 = 64

subtract 64 from each side:

s² -8s - 48 = 0

factor:

(s+4)(s-12) = 0

's equals -4 and 12 but -4 is discarded as a length so smallest side is 12