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Suppose you can buy garden fencing in lengths of 50 feet at the local hardware store. A. If you bought 100 feet of fencing and wish to enclose a rectangular garden in your backyard, what should be the dimensions of your garden in order to maximize area?

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raphealnwobi

Answer:

The answer is below

Step-by-step explanation:

Let the length of the rectangular area be L and W be the width of the rectangular garden hence:

Perimeter = 2(L + W)

There is 100 feet of fencing available which represents the perimeter, therefore:

100 = 2(L + W)

L + W = 100/2

L + W = 50  

L = 50 - W

The area (A) = L × W

A = L × W

A = (50 - W) × W

A = 50W - W²

To get maximum area, we find the first derivative of the area and equate to zero

A' = 50 - 2W

50 - 2W = 0

2W = 50

W = 50/2

W = 25 feet

100 = 2(L + W)

50 = L + W

L = 50 - W = 50 - 25

L = 25 feet

To maximize area, the length and width should be 25 feet each

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