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?

Question

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?

KnowledgeBoat · Accepted Answer

Given: Perimeter of rectangle = 36 cm Perimeter of rectangle = 2(length + breadth) ⇒ 36 = 2(length + breadth) ⇒ length + breadth = ⇒ length + breadth = 18 cm The possible pairs of (length, breadth) in natural numbers with sum 18 are: | Length | Breadth | Area (length × breadth) | | --- | --- | --- | | 17 | 1 | 17 sq. cm | | 16 | 2 | 32 sq. cm | | 15 | 3 | 45 sq. cm | | 14 | 4 | 56 sq. cm | | 13 | 5 | 65 sq. cm | | 12 | 6 | 72 sq. cm | | 11 | 7 | 77 sq. cm | | 10 | 8 | 80 sq. cm | | 9 | 9 | 81 sq. cm | (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.

Mathematics

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?

Mensuration

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Mathematics

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?

Mensuration

Related Questions

By splitting the following figures into rectangles, find their areas (The measures are given in centimetres).

How many envelopes of size 25 cm × 15 cm can be made from a rectangular sheet of size 4 m × 1.2 m?

In the adjoining figure, A, B and C are squares. If the area of the square A is 25 sq. cm and the perimeter of the square B is 12 cm, then find the perimeter and the area of the square C.

Study the following floor plan of a house prepared by an architect.Some of the measurements are given.(i) Find the missing measurements.(ii) Find out the total area of the house (including the Garden).

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?

Study the following floor plan of a house prepared by an architect.
Some of the measurements are given.
(i) Find the missing measurements.
(ii) Find out the total area of the house (including the Garden).