Question 1034612
h for hypotenuse
x for one dimension
y for other dimension
{{{system(x+y+h=12,x^2+y^2=h^2,(1/2)xy=20)}}}
See what you can find.



A way to begin may be
{{{h=12-x-y}}}
-
{{{x^2+y^2=(12-x-y)^2}}}
{{{x^2+y^2=(12-(x+y))^2=12^2-24(x+y)+(x+y)^2}}}
{{{x^2+y^2=144-24x-24y+x^2+2xy+y^2}}}
Notice x^2 and y^2 on both sides.
{{{0=144-24x-24y+2xy}}}



Continue with the system  {{{system((1/2)xy=20,24x+24y-2xy=144)}}}..............