Question 1073354
100m of wire is available for fencing a rectangular piece of land. find the 
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If the fence shape must be rectangular, then a square maximizes the enclosed area.

——  Proof that a square maximizes area ——

 Perimeter = P = 2L + 2W 
   Area = A = L*W 

A = ((P-2W)/2)*W =  (PW)/2 - W^2

dA/dW =  P/2 - 2W 
Set dA/dW = 0:   P/2 - 2W = 0  —>  W = P/4 —> L=P/4   so a square shape.
——   End proof —————

A square with sides {{{ highlight(25m)}}} will maximize the area, and that area will be {{{ 25^2 = 625m^2}}}

 
—————————————————  For fun/Info —————————————

To enclose the maximum area with no shape restrictions, a CIRCLE will do:  
Circumference= {{{ C = 2(pi)r }}}

{{{ 100 = 2(pi)r }}}
{{{ 100/(2(pi)) = r }}}
{{{ 15.915m = r }}}

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Making a circle with radius 15.915m would give you an enclosed area of {{{(pi)r^2 = 795.725m^2 }}}