find the width of a rectangle

Question

A lot is in the shape of a triangle. The shorter leg measures 60 meters. The hypotenuse is 60 meters shorter than twice the length of the longer leg. How long is the longer leg?

Answer 1

Let x be the length of the longer leg of the triangle, then:

60²+x²=(2x-60)²,

3600+x²=4x²-240x+3600,

3x²-240x=0=3x(x-80), so, since x can't be zero, x=80m, the length of the longer leg.