Question

A square lawn is surrounded by a path 2.5 m wide if the area of the path is 165m² find the area of the lawn.

Answer 1

Answer:

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Answer 2

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Consider the side of the lawn be x

Given width of the path 2.5m

Side of the lawn including path x+2(2.5)=x+5

Area of a square =(side) Consider the side of the lawn be x

Given width of the path 2.5m

Side of the lawn including path x+2(2.5)=x+5

Area of a square =(side)²

So, area of lawn = (Area of the lawn including the path) - (Area of the path)

Therefore, According to the given question,:

x²=(x+5)²-165

x²=(x²+10x+25)-165m²

x²=x²+10x+25-165

x²=x²+10x-140

x²-140=x²-10x

x²-x²-140=-10

−140=−10x

i.e 140=10x

∴x=140/10=14

Since the side of the lawn = 14m

The area of the lawn=(14)² or196 m²

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