The hypotenuse of a right triangle is 26 feet long. One leg of the triangle is 14 feet longer than the other leg. Find the lengths of the legs of the triangle.

Let the shortest leg be x feet;

The other leg will be (x + 14) feet.

Using Pythagoras theorem;

x^2 + (x+14) ^2 = 26^2

x^2 + x^2 + 28x + 196 = 676

2x^2 + 28x - 480 = 0

x^2 + 14x - 240 = 0

x^2 + 24x - 10x - 240 = 0

x (x+24) - 10 (x+24) = 0

(x+24) (x-10) = 0;

x=10;

x+14 = 24

Hence, the length of the legs are 10 feet and 24 feet.