Question

A square lawn is surrounded by a path 2.5 m wide. If the area of the path is 165 m² find the area of the lawn.

Answer 1

Area of path = 165 m²

Width of path = 2.5 m

Let the side of square lawn = x m

∴ Outer side = x + 2 × 2.5

= (x + 5) m

Expand and simplify

∴ Area of path = (x + 5)² − x²

⇒ x² + 10x + 25 − x² = 165

⇒ 10x = 165 − 25 = 140

⇒ x = `140/10` = 14 m

∴ Side of lawn = 14 m

and area of lawn = (14)² m² = 196 m²