Question

The shorter leg of a right triangle is 5in. shorter than the longer leg. the hypotenuse is 5in. longer than the longer leg. find the side lengths of the triangle.

Answer 1

15 in , 20 in , 25 in

Explanation:

let the longer leg be x , then

shorter leg = x - 5 and hypotenuse = x + 5

using Pythagoras' identity

a² + b² = c²

a , b are the legs and c the hypotenuse , then

x² + (x - 5)² = (x + 5)² ← expand factors using FOIL

x² + x² - 10x + 25 = x² + 10x + 25

2x² - 10x + 25 = x² + 10x + 25 ( subtract x² + 10x + 25 , from both sides )

x² - 20x = 0 ← factor out x from each term

x(x - 20) = 0

equate each factor to zero and solve for x

x = 0

x - 20 = 0 ⇒ x = 20

However, x > 0 , then x = 20

x - 5 = 20 - 5 = 15

x + 5 = 20 + 5 = 25

shorter leg = 15 in , longer leg = 20 in and hypotenuse = 25 in