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Question
A square lawn is surrounded by a path 2.5 m wide. If the area of the path is 165 m2 find the area of the lawn.
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Solution
Area of path = 165 m2
Width of path = 2.5 m
Let the side of square lawn = x m
∴ Outer side = x + 2 × 2.5
= (x + 5) m
Expand and simplify
∴ Area of path = (x + 5)2 − x2
⇒ x2 + 10x + 25 − x2 = 165
⇒ 10x = 165 − 25 = 140
⇒ x = `140/10` = 14 m
∴ Side of lawn = 14 m
and area of lawn = (14)2 m2 = 196 m2
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