Question 428650
Let x ft the length of one leg. Then the other leg will be: x+7 ft. Since the hypotenuse is 13 ft, we write the Pythagorean theorem:

{{{x^2+(x+7)^2=13^2}}}

{{{x^2+x^2+14x+7^2=13^2}}}, Set the equation to zero.

{{{2x^2+14x-120=0}}}, divide both sides by 2

{{{x^2+7x-60=0}}}, factor the equation. 

 (x-5)(x+12)=0 => x-5=0 => x=5 and x+12=0 => x=-12 Since the length is always positive, the root -12 is rejected.

Answer: The short leg is 5 ft and the long one is 5+7=12 ft.