Question 432784
Let the length  = {{{x}}}
The width is then {{{ (25 - 2x)/2 }}}
{{{ A = (x/2)*(25 - 2x) }}}
{{{ A = - x^2 + 12.5x }}}
The peak (maximum area) occurs at {{{x =  -b/(2a) }}}
where
{{{a = -1}}}
{{{b = 12.5}}}
{{{-b/(2a) = -12.5/(2*(-1)) }}}
{{{ x = 6.25 }}}
The length should be 6.25
and
{{{ (25 - 2x)/2 = (25 - 12.25)/2 }}}
{{{ 12.5 / 2 = 6.25 }}}
The width should be 6.25
Note that {{{6.25*4 = 25}}} and
{{{ A = 6.25^2 }}}
{{{ A = 39.0625 }}}
Here's the plot:
{{{ graph( 400, 400, -6, 16, -10, 40, -x^2 + 12.5x) }}}