JAMB - Mathematics (2001 - No. 30)

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

square of sides p

square of sides 2p

square of sides (p/2)

square of sides (p/4)

Let the rectangle be a square of sides p/4.

So that perimeter of square = 4p
4 x (p/4) = p.