SOLUTION: A square lawn is surrounded by a path 2.5m wide around it. If the area of the path is 200 square metre, find the area of lawn?

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Question 949665: A square lawn is surrounded by a path 2.5m wide around it. If the area of the path is 200 square metre, find the area of lawn?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let the side of the lawn be x meters
then total length of the side formed by the path and lawn is x+%2B+5m
So as per question
%28x%2B5%29%5E2+-+x%5E2+=+200
⇒x%5E2+%2B+10x%2B+25+-+x%5E2+=+200
⇒+10x+=+200-25
⇒+10x+=+175
⇒+x+=+175%2F10
⇒x+=+17.5m
so, area of the lawn is A=%2817.5%29%5E2+=+389.25m%5E2