To minimize fencing for Farmer George's rectangular pasture, find dimensions that meet the area requirement and minimize the perimeter using calculus techniques.
To find the dimensions that yield the least amount of fencing for Farmer George's pasture, we need to consider the formula for the area of a rectangle: Area = Length x Width. In this case, the area is 20,000 square meters. The formula for the perimeter of a rectangle is: Perimeter = 2 x (Length + Width). To minimize fencing, we need to find the dimensions that satisfy both the area requirement and minimize the perimeter.
Let's denote the length of the rectangular pasture as L and the width as W. We have two equations: L x W = 20,000 and Perimeter = 2 x (L + W). By using calculus techniques, such as optimization, we can find the dimensions that will yield the least amount of fencing for Farmer George's pasture.
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