Lacinda has 120 ft of fencing to make a rectangular kennel for her dogs. The house is to be used as one side of the kennel. What length will maximize the area of the kennel?

Since the house wall is acting as one side length of the rectangle. We are left with 1 length and 2 width sides. To maximize the Area of the kennel we will need to equally divide the 120 ft of fencing between the Length and Width.

120 / 2 = 60ft

So We have 60 ft for the length and 60 ft for the width. Since the width has 2 sides we need to divide 60 by 2.

60/2 = 30 ft

Now we can calculate the maximum Area using the values above.

[tex]A = 60*30[/tex]

[tex]A = 1800ft^{2}[/tex]

So the Maximum area we are able to create with 120ft of fencing is 1,800[tex]ft^{2}[/tex]

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raphealnwobi raphealnwobi · Answer 2 · 2022-03-11T11:13:41+01:00

A length of 30 feet would maximize the area of the kernel.

What is an area

Let l represent the length of the kernel and w represent the width of the kernel, hence:

120 = 2(l + w)

l + w = 60

w = 60 - l

The area of kernel (A) is:

A = l * w = l(60 - l)

A = 60l - l²

The maximum area is at A' = 0, hence:

A' = 60 - 2l

60 - 2l = 0

l = 30 feet

A length of 30 feet would maximize the area of the kernel.

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