The shorter leg of a right triangle is 9ft shorter than the longer leg. The hypotenuse is 9ft longer than the longer leg. Find the side lengths of the triangle

Answer 1

Let the length of the longer leg be x.

Then the shorter leg is x - 9, and the hypotenuse is x + 9.

According to the Pythagorean theorem, we have:
(x - 9)^2 + x^2 = (x + 9)^2
Expanding both sides, we get:
x^2 - 18x + 81 + x^2 = x^2 + 18x + 81
2x^2 - 18x + 81 = x^2 + 18x + 81
x^2 - 36x = 0
x(x - 36) = 0

So, x = 0 or x = 36.

Since the side length of a triangle cannot be zero, the longer leg is x = 36ft.

Therefore, the shorter leg is 36 - 9 = 27ft and the hypotenuse is 36 + 9 = 45ft.

Thus, the side lengths of the triangle are 27ft, 36ft, and 45ft.