The length of the longer leg of a right triangle is 22 ft more than six times the length of the shorter leg. The length of the hypotenuse is 23 ft more than six times the length of the shorter leg. Find the side lengths of the triangle.

Let x be the shorter leg, then the longer is 6x+22 and the hypotenuse is 6x+23.

x² + (6x+22) ² = (6x+23) ²

x² + 36x² + 264x + 484 = 36x² + 276x + 529

x² - 12x - 45 = 0

(x+3) (x-15) = 0

x=-3 or 15. since you can't have negative length discard-3, then the sides are 15, 112, and 113