solve using the Pythagorean theorem?

Question

the longer leg of a right triangle is 3ft

 longer than the shorter leg. The hypotenuse is 6ft

 longer than the shorter leg. Find the side lengths of the triangle.

Answer 1

L=3+s

h= 6+s

use the Pythagorean Theorem

hyptenuse squared = sum of the legs squared

(6+s)^2 = (3+s)^2 + s^2

36 + 12s + s^2 = 9 + 6s + s^2 + s^2

s^2 -6s -27 =0

(s-9)(s+3) = 0

s = -3 or 9

L = 12

h = 15

it's a 9-12-15 triangle

a 3-4-5 triangle inflated by a factor of 3

3(3)-3(4)-3(5)

hypotenuse = 15 feet

Longer leg = 12 feet

shortest leg = 9 feet