The hypotenuse of a right triangle is 10 ft long. The longer leg is 2 ft longer than the shorter leg. Find the side lengths of the triangle Length of the shorter leg: Length of the longer leg: Length of the hypotenuse:

To find the side lengths of the triangle, we can denote the length of the shorter leg as "x". This means the longer leg would be "x + 2". According to the Pythagorean theorem, the sum of the squares of the legs equals the square of the hypotenuse. Therefore, we have the equation: \[ x^2 + (x + 2)^2 = 10^2 \] Expanding the equation gives us: \[ x^2 + (x^2 + 4x + 4) = 100 \] Combining like terms results in: \[ 2x^2 + 4x + 4 = 100 \] Now, simplifying this gives: \[ 2x^2 + 4x - 96 = 0 \] Dividing the entire equation by 2 results in: \[ x^2 + 2x - 48 = 0 \] Factoring this quadratic, we find: \[ (x + 8)(x - 6) = 0 \] Thus, x = 6 or x = -8. Since a length can't be negative, we have: Length of the shorter leg: **6 ft** Length of the longer leg: **8 ft** Length of the hypotenuse: **10 ft** If you'd like to get a bit more context about right triangles or useful applications for them, just let me know!