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liubo4ka [24]
3 years ago
14

A farmer is constructing a rectangular pen with one additional fence across its width. Find the maximum area that can be enclose

d with 360 yards of fencing
Mathematics
1 answer:
konstantin123 [22]3 years ago
7 0

The maximum area of the pen is the highest area the pen can have

The maximum area is 16200 square yards

Let the dimension be x and y.

So, the perimeter is given as:

\mathbf{P = 360}

Because it has one additional fence, the perimeter is calculated as:

\mathbf{2x + y = 360}

Make y the subject

\mathbf{y = 360 - 2x}

The area is calculated as:

\mathbf{A = xy}

Substitute \mathbf{y = 360 - 2x}

\mathbf{A = x(360 -2x)}

Expand

\mathbf{A = 360x -2x^2}

Differentiate

\mathbf{A' = 360 -4x}

Set to 0

\mathbf{360 -4x = 0}

Rewrite as:

\mathbf{4x = 360}

Divide both sides by 4

\mathbf{x = 90}

Substitute 90 for x in \mathbf{A = 360x -2x^2}

\mathbf{A = 360 \times 90 - 2 \times 90^2}

\mathbf{A = 16200}

Hence, the maximum area is 16200 square yards

Read more about maximum areas at:

brainly.com/question/11906003

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