Question 1005005
{{{ 66/(3/4) = 88 }}} is the number of panels
Let {{{ A }}} = area of rectangle
Let {{{ w }}} = the width of rectangle
The length = {{{ ( 88 - 2w )/2 = 44 - w }}}
{{{ A = w*( 44 - w ) }}}
{{{ A = 44w - w^2 }}}
If I find the roots:
{{{ -w^2 + 44w = 0 }}}
{{{ w*( -w + 44 ) = 0 }}}
{{{ w = 0 }}} and
{{{ w = 44 }}}
are the roots
The peak of the parabola is midway between at {{{ w = 22 }}}
The length = {{{ 44 - w = 44 - 22 }}}
{{{ 44 - 22 = 22 }}}
The rectangle that maximizes area is a 22 x 22 square of panels
Here's the plot of area and number of panels
The peak is at {{{ A = 22*22 }}} which is {{{ A = 484 }}}
( measured in square panels where 1 panel is the unit of measure )
{{{ graph( 400, 400, -5, 50, -50,600, -x^2 + 44x ) }}}