Correct Answer - Option 2 : 32

**Given:**

Area of square field = 36 m^{2}

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 m^{2}

**∴ The area of the rectangular lawn is 32 m2**