Question 906014
The gardener has then 3 lengths of x and 2 lengths of y.  The fence material is distributed as {{{3x+2y=270}}}.


A(x)?  The area.

{{{A=xy}}}.
Use the fence length account equation to eliminate y.
{{{2y=270-3x}}}


{{{y=(270-3x)/2}}}
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{{{A(x)=x(270-3x)/2}}}


{{{A(x)=(270x-3x^2)/2}}}


{{{highlight(A(x)=135x-(3/2)x^2)}}}.


You can find the maximum area if you want; set {{{A(x)=0}}} and solve for x.