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A square lawn has a 2 m wide path surrounding it. If the area of the path is $136 m 2$ , find the area of the lawn.

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125 m 2

235 m 2

275 m 2

225 m 2

answer is D.

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Detailed Solution

Given a square lawn has a 2 m wide path surrounding it and the area of the path is

136 m 2

A square lawn has a 2m wide path surrounding it If the area of the path is 136m2 find the area of the lawn

Assume, side of the lawn AB = x.
Area of the square lawn

= x 2

.
From figure,

PQ = (x + 2 + 2) P Q = (x + 4) m

Area of PQRS is,

⇒ A = (x + 4) 2 ⇒ A = x 2 + 8 x + 16 m 2

Area of the path = Area of PQRS – Area of the square lawn

⇒ 136 = x 2 + 8 x + 16 − x 2

⇒ 120 = 8 x

⇒ x = 1208 ⇒ x = 15

Area of the lawn is,

A = s i d e × s i d e

⇒ A = 15 m × 15 m

⇒ A = 225 m 2

Therefore, the area of the lawn is

225 m 2

.
Hence, option 4 is correct.

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