A farmer wants to fence a rectangular area of 200 square feet next to a river. Find the length and width of the rectangle which uses the least amount of fencing if no fencing is needed along the river. Assume the length of the fence runs parallel to the river.

Step-by-step explanation:

Given

Required

The dimension to minimize cost

Area is calculated as:

This gives:

Make l the subject

The perimeter P is:

---- because one part will not be covered

Substitute:

Rewrite as:

Differentiate

Set to 0

Rewrite as:

Divide by -1

Rewrite as:

Solve for

Take square roots

Recall that:

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c. histogram

step-by-step explanation:

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