Let the side of lawn be x m.
Given that width of the path = 2.5 m
Side of the lawn including the path = (x + 2.5 + 2.5) m
= (x + 5) m
Therefore, area of lawn = (Area of the lawn including the path) – (Area of the path)
We know that the area of a square = (Side)2
Area of lawn (x2) = (x + 5)2 – 165
x2 = (x2 + 10x + 25) – 165
165 = 10x + 25
165 – 25 =10x
140 = 10x
Therefore x = 140/10 = 14
Thus the side of the lawn = 14 m
Therefore,
The area of the lawn = (14 m) 2
= 196 m2