<PRE><B>Question 175756</B>
x = length, y = width, A = area

2x + 2y = 500     isolate one variable
y = 250 - x
 
Substitude y = 250 - x.
A = xy
A = x(250 - x)
= -x^2 + 250x
 
Complete the square.
-x^2 + 250x = - (x^2 - 250x)
= - (x^2 - 250x + 15625) + 15625
= - (x - 125)^2 + 15625
 
Maximum 15625 at x = 125
 
A square will always give you the maximum area.  The maximum area is 15625m^2.  The dimensions are 125m by 125m.
 
Knowing that a square will always give you the maximum area,
 
500 / 4 = l or w
l^2 or w^2 = maximum area.

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