Question 872732
Wanting the minimum perimeter, 
dimensions x and y
xy=50 and p=2x+2y;
{{{y=50/x}}}, so substituting, {{{p=2x+2(50/x)}}}, and we have no way to distinguish between x and y.  
{{{highlight(p=2x+100/x)}}}.
{{{p=(2x^2+100)/x}}}, the minimum seems to occur near x=7, using a graphing program.


Also, using derivative of p with x,
{{{2-100*x^(-2)=0}}}
{{{2=100/x^2}}}
{{{x^2/100=1/2}}}
{{{x^2=100/2}}}
{{{x=sqrt(50)}}}
{{{x=sqrt(2*5*5)}}}
{{{highlight(x=5sqrt(2))}}}, which is approx. 7.07107
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The y value would be {{{50/(5sqrt(2))=10/sqrt(2)=10sqrt(2)/2=highlight(5sqrt(2))}}}, which is the same value as x.