The shorter leg of a right triangle is 1414 feet less than the other leg. find the length of the two legs if the hypotenuse is 3434 feet.

Let the width be x ft
the length will be (x+14) ft
hypotenuse is 34 ft
given that our triangle is right triangle, using Pythagorean theorem?
c^2=a^2+b^2
substituting our values in the formula we get:
34^2=x^2+(x+14)^2
1,156=x^2+x^2+28x+196
simplifying this we get
0=2x^2+28x-960
solving the quadratic equation we get:
x=16 or x=-30
therefore the width is 16 ft and the length is 16+14=30