Question 1041173
x y h dimensions; h for hypotenuse


{{{system(x^2+y^2=12^2,xy=24)}}}


{{{y=24/x}}}
-
{{{x^2+(24/x)^2=144}}}
{{{x^4+24=144x^2}}}
{{{x^4-144x^2+24=0}}}
Solve first for {{{x^2}}}....


Graphing y=x^4-144x^2+24 through google.com shows that there are three real and apparently rational roots, so that degree-four polynomial is factorable.