Answer:
S = 9
L = 12
H = 15
Step-by-step explanation:
So this is a system of equations. Fist, let's set up the legs.
L is longer, S is shorter and H is hypotenuse.
S = S
L = S + 3
H = S + 6
Now what equation relates all three sides of a right triangle. Pythagorean is the most obvious so let's use that.
S^2 + L^2 = H^2
S^2 + (S + 3)^2 = (S+6)^2
S^2 + S^2 + 6S + 9 = S^2 + 12S + 36
S^2 - 6S - 27
I am going to use completing the square
(S - 3)^2 - 36 = 0
(S - 3)^2 = 36
S - 3 = +/-6
S = +/-6 + 3
S = -3 or 9
Measures can't be negative so we will use 9. Plug it back into the original 3 equations.
S = 9
L = 9 + 3 = 12
H = 9 + 6 = 15
And the pythagorean theorem
9^2 + 12^2 = H^2
225 = H^2
15 = H
So it works.
