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lesya692 [45]
2 years ago
11

You have 100 feet of fencing and decide to make a rectangular garden. What is the largest area enclosed

Mathematics
1 answer:
k0ka [10]2 years ago
3 0

Answer:

625 ft^2

Step-by-step explanation:

Given

P = 100 --- perimeter

Required

The largest area

The perimeter is calculated as:

P = 2 * ( L + W)

So, we have:

2 * ( L + W) = 100

Divide both sides by 2

L + W  = 50

Make  L the subject

L = 50 - W

The area is calculated as:

A= L * W

Substitute L = 50 - W

A= (50 - W) * W

Open bracket

A = 50W - W^2

Differentiate with respect to W

A' = 50 -2W

Set to 0; to get the maximum value of W

50 - 2W = 0

Collect like terms

-2W = -50

Divide by -2

W = 25

So, the maximum area is:

A = 50W - W^2

A = 50 * 25 - 25^2

A = 1250 - 625

A = 625

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