Question 173498
Short leg:  {{{x}}}
Long leg:  {{{2x+20}}}
Hypotenuse: {{{2x+30}}}


Pythagoras says:


{{{x^2+(2x+20)^2=(2x+30)^2}}}


Expand the binomials:


{{{x^2+4x^2+80x+400=4x^2+120x+900}}}


Add {{{-4x^2-120x-900}}} to both sides:


{{{x^2+4x^2-4x^2+80x-120x+400-900=0}}}


Collect terms:


{{{x^2-40x-500=0}}}


Solve the quadratic.  Hint:  {{{(10)(-50)=-500}}} and {{{10+(-50)=-40}}}


One of your roots will be negative.  This is an extraneous root created when we squared the variable in the process of solving the problem, so discard it.  The positive root will be the measure of the shorter leg.  The other two length measures should be simple to calculate from the relationships in the problem givens.