Question

On a centimeter squared paper, make as many rectangle as you can, such that the area of the rectangle is 64 sq.cm (consider only natural number lengths). 

(i) Which rectangle has the greatest perimeter? 

(ii) Which rectangle has the least perimeter? 

(iii) Find the change in the width of rectangle with decreasing perimeter of the rectangle.

Answer 1

Following be the length and breadth of rectangle to find 64 sq. cm.

Area:

(a) Perimeter = 2 (64 + 1 ) = 2 (65) = 130 cm 

(b) Perimeter = 2 (32 + 2) = 2 (34) = 68 cm 

(c) Perimeter = 2 (16 + 4) = 2 (20) = 40 cm 

(d) Perimeter = 2 (8 + 8) = 2 (16) = 32 cm

• Perimeter of rectangle (a) is greatest (130 cm) whose length is 64 cm and breadth is 1 

• Perimeter of rectangle (d) is least (32 cm). Whose length is 8 and breadth is 8 cm. Its also called square. 

• Perimeter decreased as breadth of rectangle increased.