Question

A square lawn is surrounded by a path that is 2.5m wide. If the area of the path is 165m² wide, find the area of the lawn.​

Answer 1

Let 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 square=side square

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

Answer 2

Answer:

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