The longer leg of a right triangle is 3 ft longer than the shorter leg. The hypotenuse is 6 ft longer than the shorter leg. Find the side lengths of the triangle.

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.  

2nd one in the first row is correct