Question 581762: Suppose a farmer has 1000m of fencing to enclose a rectangular
field. What is the largest area that the farmer can enclose?
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! The Perimeter is:
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The Area is:
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First of all, when the coefficient of the
squared term is negative, then there is a maximum
and not a minimum.
When the equation is in the form
 , the max or min is
always at  , or, in this case,
and I know that
The largest area that the farmer can enclose
is  = 62,500 ft2
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I can prove this by changing the dimensions
slightly, but still keeping the same Perimeter
 = 62,499 ft2
 = 62,496 ft2 ( even less )
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