a square lawn is surrounded by a path 2.5 metre wide the area of the path is 165 metre square find the area of the Lawn
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Answer:
(14)2 or 196 m2.
Step-by-step explanation:
Answer.
Consider the side of the lawn be x
Given width of the path = 2.5m
Side of the lawn including path = x + 2(2.5m) = x + 5m
So, area of lawn = (Area of the lawn including the path) - (Area of the path)
Area of a square = (side)2
Therefore, we say :
x2 = (x + 5)2 – 165 m2
x2 = (x2 + 10x +25) - 165m2
x2 = x2+ 10x + 25 - 165
x2 = x2 + 10x - 140
x2 - 140 = x2 - 10x
x2 - x2 - 140 = -10x
-140 = -10x
i.e 140 = 10x
Therefore x = 140/10 = 14
Since the side of the lawn = 14 m
The area of the lawn = (14)2 or 196 m2.
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