Question 503181
If one side is  {{{x}}}, the opposite side is also {{{x}}}
Their sum is {{{2x}}}
Call the other 2 sides {{{y}}}
Call the perimeter {{{P}}}
{{{ P = 2x + 2y }}}
solve for {{{y}}}
{{{ 2y = P - 2x }}}
{{{ y = (P/2) - x }}}
And, since {{{ P = 600 }}},
{{{ y = 300 - x }}}
The area os the rectangle is {{{ A = x*y }}}
{{{ A = x*( 300 - x ) }}}
{{{ A = 300x - x^2 }}}
Here's a plot of area and x:
{{{ graph( 400, 400, -40, 330, -1000, 25000 , 300x - x^2) }}}