Question 969490
If the pens measure x by y then the
perimeter of each is {{{ 2x + 2y }}}
The perimeters of {{{ 6 }}} pens measure
{{{ 6*( 2x + 2y ) = 12*( x + y ) }}}
{{{ 12*( x + y ) = 900 }}}
{{{ x + y = 75 }}}
{{{ y = 75 - x }}}
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{{{ A = x*y }}}
{{{ A = x*( 75 - x ) }}}
{{{ A = -x^2 + 75x }}}
This is a parabola which is maximum when
{{{ x[max] = -b/(2a) }}}
{{{ x[max] = -75/(2*(-1) ) }}}
{{{ x[max] = 37.5 }}}
and
{{{ y = 75 - x }}}
{{{ y = 37.5 }}}
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To maximize area, the dimensions of
each pen are: 37.5 x 37.5 
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Here is a plot of the function {{{ A = -x^2 + 75x }}}
{{{ graph( 400, 400, -10, 90, -200, 1500, -x^2 + 75x ) }}}