Question 123179
Call the one side, x.
THe other side is then x+2.
From the Pythagorean theorem, you know that 
{{{x^2+(x+2)^2=12^2}}}
{{{x^2+(x^2+4*x+4)=144}}}Expand the perfect square. 
{{{2x^2+4x+4=144}}}Simplify.
{{{2x^2+4x-140=0}}}Bright all terms to one side. 
{{{x^2+2x-70=0}}}Divide by 2.
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} Use the quadratic equation.
{{{x = (-2 +- sqrt( 2^2-4*1*(-70) ))/(2*1) }}} 
{{{x = (-2 +- sqrt( 4+280))/(2) }}} 
{{{x = (-2 +- sqrt(284))/(2) }}}
{{{x[1] = (-2 + sqrt(284))/(2) }}}
{{{x[2] = (-2 - sqrt(284))/(2) }}}
{{{x[1] = 7.43}}}
{{{x[2] = -9.43}}}
Since a negative length does not make sense in this application, use only the positive results. 
x=7.43
x+2=9.43
Check the results to verify your answer.
{{{x^2+(x+2)^2=12^2}}}
{{{(7.43)^2+(9.43)^2=12^2}}}
{{{55.2049+88.9249=144}}}
{{{144.1298=144}}}
Look likes that close enough.