Question:
A square lawn is surrounded by a 2.5 m wide path. If the area of the path is 165m. Find the area of the lawn.
Answer:
Let length of side of lawn = x
So, the area of the lawn = x*x = x2
Now, given width = 2.5 m
So, the length increased by 2.5 + 2.5 = 5 m
Now, area of the path including width = (x + 5)*(x + 5)
Given, area of the path = 165
=> (x + 5)*(x + 5) - x2 = 165
=> x2 + 10x + 25 - x2 = 165
=> 10x + 25 = 165
=> 10x = 165 - 25
=> 10x = 140
=> x = 140/10
=> x = 14
So, the side of the lawn = 14 m
Hence, area of the lawn = (14)2 = 196 m2
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