Question 225108
Let the two legs be x and x+1, then from the Pythagorean theorem, we have:
{{{x^2+(x+1)^2 = 5^2}}}
{{{x^2+(x^2+2x+1) = 25}}}
{{{2x^2+2x+1 = 25}}} Subtract 25 from both sides.
{{{2x^2+2x-24 = 0}}} Factor out a 2.
{{{2(x^2+x-12) = 0}}} so...
{{{x^2+x-12 = 0}}} Factor this quadratic equation.
{{{(x+4)(x-3) = 0}}} and...
{{{x = -4}}} or {{{x = 3}}} Discard the negative solution as lengths are positive.
{{{x = 3}}} and {{{x+1 = 4}}}
The two legs are 3 inches and 4 inches.