Question 961523
Known:  A, area and p, perimeter of a rectangle.

Unknown: x and y dimensions.


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


{{{2x^2/x+2A=px}}}
{{{2x^2-px+2A=0}}}
and you can continue with this in symbolic form, but you can find the specific result for your example faster if you substitute the given A and p NOW.


{{{2x^2-48x+2*40=0}}}
{{{x^2-24x+40=0}}}
START FIX:  {{{x=(24+- sqrt(24^2-4*40))/2}}}
{{{x=(24+- sqrt(416))/2}}}
416=4*104=4*2*52=4*2*4*13=4^2*26
{{{x=(24+- sqrt(4^2*26))/2}}}
{{{x=(24+- 4sqrt(26))/2}}}
{{{highlight_green(x=12+- 2sqrt(26))}}}


Take your pick for which dimension is x and which is y; but the two dimensions are {{{highlight(12-2sqrt(26))}}} and {{{highlight(12+2sqrt(26))}}}.