The perimeter of a rectangle is 36 cm. What will be length and breadth (in natural numbers) of that rectangle whose area is

(i) maximum?

(ii) minimum?

Given:

Perimeter of rectangle = 36 cm

Perimeter of rectangle = 2(length + breadth)

⇒ 36 = 2(length + breadth)

⇒ length + breadth = $\dfrac{36}{2}$

⇒ length + breadth = 18 cm

The possible pairs of (length, breadth) in natural numbers with sum 18 are:

(i) The maximum area is 81 sq. cm when length = 9 cm and breadth = 9 cm.

Hence, for maximum area, length = 9 cm and breadth = 9 cm.

(ii) The minimum area is 17 sq. cm when length = 17 cm and breadth = 1 cm.

Hence, for minimum area, length = 17 cm and breadth = 1 cm.