Question 575194
This can be done without calculus.
 I assume this is pre-calculus.
Let the sides be {{{ x }}}, {{{x }}}, {{{ y }}}, and {{{y}}}
Let {{{ A }}} = area
{{{ 2x + 2y = 500 }}}
{{{ 2y = 500 - 2x }}}
{{{ y = 250 - x }}}
{{{ A = x*( 250 - x ) }}}
{{{ A = 250x - x^2 }}}
Because of the minus in front of the {{{ x^2 }}} term,
this curve has a maximum and not a minimum.
The maximum occurs at {{{x =  -(b/(2a)) }}} when the
equation has the form {{{ a*x^2 + b*x + c }}}
{{{ a = -1 }}}
{{{ b = 250 }}}
{{{ -(b/(2a)) = -( 250/(2*(-1))) }}}
{{{x =  125 }}}
and
{{{ y = 250 - x }}}
{{{ y = 250 - 125 }}}
{{{ y = 125 }}}
So the dimensions that maximize the area are  A = 125 x 125
which is a square. ( This is always true when you are maximizing a
rectangular area )