Question

A square field whose area is 36 m² and a rectangular lawn whose width is \(\dfrac{2}{3}\) of the side of square field have the same perimeter. The area (in m²) of the lawn is
1. 24
2. 32
3. 48
4. 64

Answer 1

Correct Answer - Option 2 : 32

Given:

Area of square field = 36 m²

Width of rectangular lawn = (2/3) × Side of square field

Perimeter of rectangular lawn = Perimeter of square field 

Formula used:

Perimeter of rectangle = 2 × (Length + Breadth)

Perimeter of square = 4 × Side of square

Area of rectangle = Length × Breadth 

Area of square = (Side of square)²

Calculations:

Let the length of the rectangular lawn be x m

Area of square field, 

⇒ (Side of square)² = 36

⇒ Side of square = 6 m

Width of rectangle = (2/3) × 6

⇒ 4 m

Perimeter of square field = 4 × 6

⇒ 24 m

Perimeter of rectangular lawn = 24 m

⇒ 2 × (4 + x) = 24

⇒ 4 + x = 12

⇒ x = 8 m

Area of rectangular lawn = 4 × 8

⇒ 32 m²

∴ The area of the rectangular lawn is 32 m2