The Longer leg of a right triangle is 7ft longer than the shorter leg. The hypotenuse is 9ft longer than the shorter leg. Find the side lengths of the triangle.
Let x be the length of the shorter leg.
The longer leg is x + 7.
The hypotenuse is x + 9.
Using the Pythagorean theorem, we have:
x^2 + (x + 7)^2 = (x + 9)^2
Expanding both sides, we get:
x^2 + x^2 + 14x + 49 = x^2 + 18x + 81
Simplifying further:
2x^2 + 14x + 49 = x^2 + 18x + 81
Rearranging terms:
x^2 - 4x - 32 = 0
Factoring the quadratic equation, we get:
(x - 8)(x + 4) = 0
So, x is either 8 or -4. Since the length of a side of a triangle cannot be negative, the shorter leg is 8 ft.
Therefore, the longer leg is 8 + 7 = 15 ft, and the hypotenuse is 8 + 9 = 17 ft.
The side lengths of the triangle are 8ft, 15ft, and 17ft.