Question 949665

 let the side of the lawn be {{{x}}} meters
then total length of the side formed by the path and lawn is {{{x + 5m}}}
So as per question

{{{(x+5)^2 - x^2 = 200}}}

⇒{{{x^2 + 10x+ 25 - x^2 = 200}}}

⇒{{{ 10x = 200-25}}}

⇒{{{ 10x = 175}}}

⇒{{{ x = 175/10}}}

⇒{{{x = 17.5m}}}

so, area of the lawn is {{{A=(17.5)^2 = 389.25m^2}}}