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So let the side of the lawn be x m
so total length of the side formed by the path and lawn is x + 5 m
So as per question
(x+5)² - x² = 200
⇒x² + 25 + 10x - x² = 200
⇒x = 17.5 m

so area of the lawn is (17.5)² = 389.25 m² ANSWER