SOLUTION: Suppose a farmer has 1000m of fencing to enclose a rectangular field. What is the largest area that the farmer can enclose?

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:

-------------------
The Area is:

--------------------
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
-------------------------------
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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