Question 190580
Let x be the length of the shorter leg, then the longer leg is x+2.
Using the Pythagorean theorem {{{c^2 = a^2+b^2}}}, we can write:
{{{10^2 = x^2+(x+2)^2}}} Simplifying, we get:
{{{100 = 2x^2+4x+4}}} Subtracting 100 from both sides and rearranging, we have:
{{{2x^2+4x-96 = 0}}} This can be factored into...
{{{2(x^2+2x-48) = 0}}}  so...
{{{x^2+2x-48 = 0}}} Factor this into...
{{{(x-6)(x+8) = 0}}} Applying the zero product rule...
{{{x-6 = 0}}} or {{{x+8 = 0}}} so that...
{{{x = 6}}} or {{{x = -8}}} Discard the negative solution as lengths are positive quantities.
{{{x = 6}}}
The shorter leg is 6 feet.