A rectangular field is to be fenced off, and then divided into two by a fence running parallel to one of the sides. If 744 meters of fencing can be used, find the maximum area that can be enclosed by the fence.\

Explanation:

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Maximum area enclosed by the fence= 23,064 m²

Explanation:

Size of the fence used = 744m

Let the width of the fence be y

If the fence is divided into two by a fence running in parallel to one side of the fence, then the length, L = (744 - 3y)/2

Area enclosed by the fence, A = Length * Breadth

A = (744 - 3y)/2  *  y

A = 372y - 1.5y²

At maximum area, A'(y) = 0

A'(y) = 372 - 3y

372 - 3y = 0

y = 372/3

y = 124 meters

Maximum area enclosed by the fence = 372(124) - 1.5*124²

A = 46128 - 23064

Maximum area = 23,064 m²

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