First, let's set up the legs:
Let L be the longer leg, S the shorter and H the hypothenuse:
S = S
L = S + 3
H = S + 6
The triangle is a right triangle, so, using Pythagorean Theorem:
Replacing H, L and S values on the formula:
Solving the expression:
S² + 12S + 36 = S² + S² + 6S + 9
S² - 6S - 27 = 0
(S - 9)(S + 3)
S = -3 or S = 9
Measures can't be negative so we will use 9. Plug it back into the original 3 equations:
S = S
S = 9 (length of the shorter leg)
L = S + 3
L = 9 + 3
L = 12 (length of the longer leg)
H = S + 6
H = 9 + 6
H = 15 (length of the hypotenuse)