Math CentralQuandaries & Queries


Question from Darlene, a parent:

A farmer has 10,000 meters of fencing to use to create a rectangular field. He plans on using some of the fencing to divide the rectangular field into two plots of land by constructing a fence inside the rectangle that is parallel to one of the sides. Let X be the width of the rectangular field. Write an equation to express the area of the field as a function of X. Find the value of X that maximizes the area of the field.

Hi Darlene,

I drew a diagram of the field.


The width of the field is $x$ meters and hence, so far the farmer has used $3 \times x$ meters of fencing. He started with 10,000 meters of fencing so how much does he have left? This amount has to be divided in half to get two pieces of fending for the other sides. Now you know the length and width of the field so what is its area?


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