The hypotenuse of a right triangle is 13 cm long. The longer leg is 7cm longer that the shorter leg. Find the side lengths of the triangle
Let the shorter leg be x cm long.
Then, the longer leg is x + 7 cm long.
Using the Pythagorean theorem, we have:
x^2 + (x + 7)^2 = 13^2
x^2 + x^2 + 14x + 49 = 169
2x^2 + 14x - 120 = 0
x^2 + 7x - 60 = 0
(x + 12)(x - 5) = 0
x = 5 (since side lengths of a triangle cannot be negative)
Therefore, the shorter leg is 5 cm long and the longer leg is 12 cm long.