# Calculus

What are the dimensions of a rectangular field of area A that requires the least amount of fencing?

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1. a square

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2. Are you saying that the answer is lw?

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3. Does this problem have a solution? Could you please type it in for me. Thanks! :)

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4. Huh, you can't figure the dimensions of s square of area A?

The maximum area for a given perimeter is a square.

The minimum perimeter for a given rectangular area is a square.

So, the length and width would both be √A

But, since you seem to be taking calculus, look at the dimensions. If the width is x, the length is A/x

The perimeter is
p = 2(x + A/x)
dp/dx = 2(1 - A/x^2)
dp/dx = 0 when 1 - A/x^2 = 0
That is, when x = √A

as we started out.

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