Question

The hypotenuse of a right triangle is 13 ft long. The shorter leg is 7 ft shorter than the longer leg. Find the side lengths of the triangle.

Answer 1

Since the length of a side of a triangle must be a positive number, the only solution that makes sense is $x = \frac{14 + \sqrt{-764}}{8}$. The length of the shorter leg is then $y = x - 7 = \frac{14 + \sqrt{-764}}{8} - 7 = \frac{7 + \sqrt{-764}}{8}$.

Therefore, the side lengths of the triangle are $\frac{7 + \sqrt{-764}}{8}$ and $\frac{14 + \sqrt{-764}}{8}$.