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 120m . 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