Question 1085701
Circumference is a term reserved for the perimeter of a circle.
I'm assuming you mean the perimeter of the rectangle.
{{{P=2(L+W)}}}
{{{2(L+W)=100}}}
{{{L+W=50}}}
{{{L=50-W}}}
and
{{{LW=1}}}
Substituting from above,
{{{(50-W)W=1}}}
{{{-W^2+50W=1}}}
{{{W^2-50W+1=0}}}
{{{(W^2-50W+625)+1=625}}}
{{{(W-25)^2=624}}}
{{{W-25=0 +- sqrt(624)}}}
{{{W=25+-4sqrt(39)}}}
So then,
{{{L=50-(25+-4sqrt(39))}}}
{{{L=25 +- 4sqrt(39)}}}
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So the two sides of the rectangle are {{{25-4sqrt(39)}}} and {{{25+4sqrt(39)}}}.