Question

A square lawn has a 2-m-wide path surrounding it. If the area of the path is 136 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 one side of the lawn (AB) be x m.
Area of the square lawn = x²
Length PQ = (x m + 2 m + 2 m) = (x + 4) m
∴ Area of PQRS = (x + 4)² = (x² + 8x + 16) m²

Now, Area of the path = Area of PQRS − Area of the square lawn
⇒ 136 = x² + 8x + 16 − x²
⇒ 136 = 8x + 16
⇒ 136 − 16 = 8x
⇒ 120 = 8x
∴ x = 120 ÷ 8 = 15
∴ Side of the lawn = 15 m

∴ Area of the lawn = (Side)² = (15 m)² = 225 m²