Question 1089557
Let {{{ x }}} = the length of the side which is
perpendicular to the street
{{{ 236 - 2x }}} = the length of fence which is
parallel to the street
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Let {{{ A }}} = the area of the lot
{{{ A = x*( 236 - 2x ) }}}
{{{ A = -2x^2 + 236x }}}
The formula for the vertex, which in this case 
is a maximum is:
{{{ x[max] = -b/(2a) }}}
{{{ x[max] = -236 / ( 2*(-2)) }}}
{{{ x[max] = 59 }}}
and
{{{ A[max] = -2*59^2 + 236*59 }}}
{{{ A[max] = -2*3481 + 13924 }}}
{{{ A[max] = -6962 + 13924 }}}
{{{ A[max] = 6962 }}}
The maximum area is 6,962 ft2
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check:
Here's the plot:
{{{ graph( 400, 400, -15, 150, -800, 8000, -2x^2 + 236x ) }}}