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Find the dimensions of a rectangle of greatest area which has a fixed perimeter \(p.\)...


Question

Find the dimensions of a rectangle of greatest area which has a fixed perimeter \(p.\)

Options

A) square of sides \(p\)

B) square of sides \(2p\)

C) square of sides \(\frac{p}{2}\)

D) square of sides \(\frac{p}{4}\)

Explanation:

Let the rectangle be a square of sides \(\frac{p}{4}.\)
So that perimeter of square \(= 4p\)
\(4 \times \frac{p}{4} = p.\)


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