Question 930356
{{{P=2(L+W)=36}}}
{{{L+W=18}}}
{{{L=18-W}}}
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{{{A=L*W}}}
{{{A=(18-W)W}}}
{{{A=18W-W^2}}}
{{{A=-(W^2-18W+81)+81}}}
{{{A=-(W-9)^2+81}}}
The vertex is ({{{9}}},{{{81}}}).
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The graph isn't really required only the vertex form of the equation.
Since there is a {{{-1}}} multiplier in front of the quadratic term, the parabola opens downwards so the vertex value is the maximum. 
So you know the width ({{{W=9}}}) at the maximum area ({{{A=81}}}). 
Then you also know the length {{{L=18-W=18-9=9}}}.
So the maximum area rectangle is a square.