Correct Answer - Option 2 : 5 m

**Given:**

A path of uniform width runs round inside the rectangular field of 38 m long and 32 m wide. if the path occupies 600 m^{2}.

**Concept used:**

Area of rectangle = Length × Breadth

**Calculation:**

Let the width of path be x m.

Area of rectangular field = 38 × 32 = 1216 m^{2}

Area of rectangular field without path = (38 - 2x) (32 - 2x)

⇒ 1216 - 64x - 76x + 4x^{2}

⇒ 4x^{2} - 140x + 1216

Area of path

⇒ 1216 - (4x^{2} - 140x + 1216)

⇒ 140x - 4x^{2}

The path of the rectangular field occupies is 600 m^{2}

⇒ 140x - 4x^{2} = 600

⇒ 4x^{2} - 140x + 600

⇒ x^{2} - 35x + 150

⇒ x^{2} - 30x - 5x + 150

⇒ x(x - 30) - 5(x - 30)

⇒ (x - 5) (x - 30)

∴ x = 5 because \(x \ne 30\)

∴ **x = 5m is the width of the path. **