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A square lawn is surrounded by a path 2.5 m wide. If the area of the path is $165 m 2$ , find the area of the lawn.

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196 m 2

126 m 2

136 m 2

146 m 2

answer is A.

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Detailed Solution

Given a square lawn is surrounded by a path 2.5 m wide and the area of the path is

165 m 2

.
Assume, side of the square = x.
Side of square lawn with path = x + 2.5 + 2.5
Area of square =

s i d e 2

Area of square = area of square lawn with path – area of path

x 2 = x + 2.5 + 2.5 × x + 2.5 + 2.5 − 165

⇒ x 2 = x + 5 2 − 165

⇒ x 2 = x 2 + 25 + 10 x − 165

⇒ 10 x + 25 = 165

⇒ 10 x = 165 − 25

⇒ 10 x = 140

⇒ x = 14

The area is,

⇒ 14 × 14

⇒ 196 m 2

Therefore, the area of the square field is

196 m 2

.
Hence, option 1 is correct.

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