The hypotenuse of a right triangle is 24ft long. The length of one leg is 20ft more than the other. Find the length of the legs.

By the Pythagorean Theorem, the hypotenuse squared is equal to the sum of the sides squared ...

h^2=x^2+y^2

We are told that y=x+20 and h=24 so

x^2 + (x+20) ^2=24^2

x^2+x^2+40x+400=576

2x^2+40x+400=576

2x^2+40x=176

x^2+20x=88

x^2+20x+100=188

(x+10) ^2=188

x+10=±√188

x=-10±√188, x>0 so

x=-10+√188 ft

y=10+√188 ft

If you want approximations ...

x≈3.71 ft

y≈23.71 ft