Question

A farmer with 1200 meters of fencing wishes to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. What are the dimensions of the field that produce the largest area

1. The perimeter of a given figure is a measure of the addition of each individual length of the sides of the figure. Thus the dimensions that would produce the largest area of the field are; length = 300 m, and width = 200 meters.
The perimeter of a given figure is a measure of the addition of each length of the sides of the figure. It always has the unit as that of the given sides of the figure.
So in the given question, the perimeter of the fence required = 1200 meters.
Thus, let the length of the enclosed rectangle be represented by l and its width by w. Thus,
Perimeter = 2l + 3w
1200 = 2l + 3w
Thus, let l be equal to 300, we have;
1200 = 2(300) + 3w
1200 – 600 = 3w
w = 200
Thus the dimensions of the field that would produce the largest area are; length = 300 m and width = 200 m.
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