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

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 Geometry: Rectangles Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Rectangles 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(9671)   (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 )