Question 628179
The formula for perimeter is
{{{ P = 2L + 2W }}}
given:
{{{ P = 4 }}} cm
{{{ 4 = 2L + 2W }}}
{{{ 2 = L + W }}}
{{{ W = 2 - L }}}
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The formula for area is
{{{ A = W*L }}}
By substitution:
{{{ A = ( 2 - L )*L }}}
{{{ A = -L^2 + 2L }}}
This is a parabola with {{{A}}} plotted on the
vertical axis and {{{ L }}} on the horizontal.
The minus sign in front of {{{ L^2 }}} means
the parabola has a maximum, not a minimum.
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If the equation has the form {{{ f(L) = a*L^2 + b*L + c }}},
then the {{{ L }}} coordinate of the maximum is at
{{{ -b/(2a) }}}
{{{ a = -1 }}}
{{{ b = 2 }}}
{{{ L[max] = -2/(2*(-1)) }}}
{{{ L[max] = 1 }}}
So, the max is at ( 1,A ) where {{{ A }}} is
{{{ A = -1^2 + 2*1 }}}
{{{ A = -1 + 2 }}}
{{{ A = 1 }}} 
The maximum area is 1 cm2
and, if {{{ L=1 }}}, then
{{{ W = 2 - L }}}
{{{ W = 2 - 1 }}}
{{{ W = 1 }}}
So the maximum area is when the rectangle is a square
with {{{ L=W=1 }}}