Question

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

(i) Which rectangle has the greatest area? 

(ii) Which rectangle has the least area? 

(iii) Find the change in length of rectangle with increasing area of the rectangle.

Answer 1

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

(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 

• Area of rectangle (d) is greatest (16 sq. cm) whose length is 4 cm and breadth is 4 cm. Its also called square. 

• Area of rectangle (a) is least (7 sq. cm), whose length is 7 cm and breadth is 1 cm. 

• Area increased as length of rectangle decreased.