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

Let ABCD be the square lawn and PQRS be the outer boundary of the square path.

Let a side of the lawn (AB) be x m.
Area of the square lawn = x²
Length, PQ = (x m + 2.5 m + 2.5 m) = (x + 5) m
∴ Area of PQRS = (x + 5)² = (x² + 10x + 25) m²

Area of the path = Area of PQRS − Area of the square lawn (ABCD)
⇒ 165 = x² + 10x + 25 − x²
⇒ 165 = 10x + 25
⇒ 165 − 25 = 10x
⇒ 140 = 10x
∴ x = 140 ÷ 10 = 14
∴ Side of the lawn = 14 m

∴ Area of the lawn = (Side)² = (14 m)² = 196 m²