Question

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.

Answer 1

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