A rectangular fie

Length of the rectangular field = 20m

Breadth of the rectangular field = 14m

Let x be the uniform width all around the path.

Length of the rectangular field including the path

= 20 + x + x

= 20 + 2x

Width of the rectangular field including path

= 14 + x + x

= 14 + 2x

Area of path = area of rectangular field including path – area of rectangular field

⇒ 111 = (20 + 2x)(14 + 2x) – (20 × 14)

⇒ 111 = 280 + 40x + 28x + 4x² – 280

⇒ 111 = 68x + 4x²

⇒ 4x² + 68x – 111 = 0

⇒ 4x² + 74x – 6x – 111 = 0

⇒ 2x(2x + 37) – 3(2x + 37) = 0

⇒ (2x + 37)(2x – 3) = 0

2x + 37 = 0 or 2x – 3 = 0

2x = –37 or 2x = 3

x = –18.5 or x = 1.5

Therefore, width of the path = 1.5m