Question 935989
Dimensions x and y and are unknown.
A and p are known area and perimeter.


{{{system(xy=A,2x+2y=p)}}}


{{{2y=p-2x}}}
{{{y=p/2-x}}}
-
xy=A
{{{x(p/2-x)=A}}}
{{{(p/2)x-x^2=A}}}
{{{px-2x^2=2A}}}
{{{-2x^2+px=2A}}}
{{{2x^2-px=-2A}}}
{{{2x^2-px+2A=0}}}, you can probably factor the quadratic member when the values for p and A are used, but you do not always know.  Examples vary.


{{{x=(p+- sqrt(p^2-4*2*2A))/(2*2)}}}
{{{highlight(x=(p+- sqrt(p^2-16A))/(2*2))}}}


I leave the rest of the work and decisions to you.