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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 $$= 4p$$
$$4 \times \frac{p}{4} = p.$$

## Dicussion (1)

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