The hypotenuse of a 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

I'm assuming this is a right angled triangle
By Pythagoras:_

x^2 + (x + 14)^2 = 26^2    where x = length of the shortest leg

x^2 + x^2 + 28x + 196 =  676

2x^2 + 28x -  480 = 0

x^2 + 14x - 240 = 0

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

so shortest side  x = 10 feet  ( we ignore the negative root)

So the lengths of the legs  is 10 and 24 feet.