Question

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.

Answer 1

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.