Paul has 400 yards of fencing to enclose a rectangular area. find the dimensions of the rectangle that maximize the enclosed area. what is the maximum area?

a rectangle that maximizes the enclosed area has a length of _ nothing yards and a width of _ nothing yards.

the maximum area is _ nothing square yards.

The area of a shape is the amount of space it occupies.

The perimeter is given as:

The perimeter of the fence is calculated as:

Where

L and W are the length and width of the fence

So, we have:

Divide both sides by 2

Make L the subject

The area of a rectangle is:

Substitute

Differentiate, and set to 0

Set to 0

Collect to 0

Divide by 2

Recall that:

The area of the fence is:

Hence,

The dimension that maximizes the area is 100 yards by 100 yards, and the maximum area is 10000 square yards

Read more about areas at:

link

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step-by-step explanation:

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