Question

On a centimetre squared paper, make as many rectangles as you can, such that the area of the rectangle is 16 sq cm (consider only natural number lengths).

1. Which rectangle has the greatest perimeter?
2. Which rectangle has the least perimeter?
3. If you take a rectangle of an area of 24 sq cm, what will be your answers?

Answer 1

Following the length and breadth of the rectangle to find a 16 cm perimeter

Rectangle	a	b	c	d
l	7	6	5	4
b	1	2	3	4

(a) Area = l × b = 7 × 1 = 7 sq. cm

(b) Area = l × b = 6 × 2 = 12 sq. cm

(c) Area = l × b = 5 × 3 = 15 sq. cm

(d) Area = l × b = 4 × 4 = 16 sq. cm 

• The area of a rectangle (d) is greatest (16 sq. cm) whose length is 4 cm and breadth is 4 cm. It's also called square.
• The area of the rectangle (a) is least (7 sq. cm), whose length is 7 cm and breadth is 1 cm. 
• The area increased as the length of the rectangle decreased.