Question 588428
The formula for perimeter of a rectangle is
{{{ P = 2L + 2W }}}
The formula for Area is 
{{{ A = L*W }}}
----------
given:
{{{ P = 30 }}} cm
{{{ 30 = 2L + 2W }}}
{{{ 2W = 30 - 2L }}}
{{{ W = 15 - L }}}
Substitute this into {{{A}}}
{{{ A = L*( 15 - L ) }}}
{{{ A = -L^2 + 15L }}}
Here's a plot of this equation. 
{{{L}}} is on the horizontal axis
 {{{ graph( 400, 400, -4, 20, -4, 60, -x^2 + 15x ) }}}
The value of {{{L}}} that gives a maximum {{{A}}}
is {{{ -b/(2a) = -15/(2*(-1)) }}}
{{{ -b/(2a) = 7.5 }}}
The rectangle with maximum area is a
square with sides  = 7.5 cm
{{{ 7.5*7.5 = 56.25 }}} cm2
The minimum area is 15 cm2