Question

A 30 centimeters long rope is used to make a rectangular plot. If the length to width ratio is 1 : 2, what is the area of the rectangle?

What if this ratio is 2 : 3?

Answer 1

(i) Ratio of length to width of the rectangle = 1 : 2

Total length of the rope = 30 cm

⇒ Perimeter of rectangular plot = 30 cm

⇒ 2(l + b) = 30

⇒ l + b = 15

Let the length of the rectangular plot be x cm and breadth be 2x cm.

⇒ x + 2x = 15

⇒ x = 5

∴ Length of the rectangle = 5 cm

Width of the rectangle = 2 × 5 cm = 10 cm

Area of the rectangle = Length × width

= 5 cm × 10 cm

= 50 cm²

(ii) Ratio of length to width of the rectangle = 2 : 3

Total length of the rope = 30 cm

⇒ Perimeter of rectangular plot = 30 cm

⇒ 2(l + b) = 30

⇒ l + b = 15

Let the length of the rectangular plot be 2x cm and breadth be 3x cm.

⇒ 2x + 3x = 15

⇒ x = 3

Length of the rectangle = 2 × 3 cm = 6 cm

Width of the rectangle = 3 × 3 cm = 9 cm

Area of the rectangle = Length × width

= 6 cm × 9 cm

= 54 cm²