Question

A rectangular field is 16 m long and 10 m wide. There is a path of uniform width all around it, having an area of 120 m². Find the width of the path.

Answer 1

Let the uniform width of the path be x m.

Original length = 16 m

Original width = 10 m

New length = 16 + 2x

New width = 10 + 2x

Area of path = Area of outer rectangle – Area of field

Given area of path = 120 m²

(16 + 2x) (10 + 2x) – (16 × 10) = 120

(16 + 2x) (10 + 2x) = 160 + 120 = 280

160 + 32x + 20x + 4x² = 280

4x² + 52x + 160 = 280

4x² + 52x – 120 = 0

x² + 13x – 30 = 0

(x + 15) (x – 2) = 0

The width of the path is 2 m.