a square lawn is surrounded by a path 2m wide around it. if the area of the path is 120m2 find the area of the lawn.
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Let the side of lawn be 'a' m.
Area of lawn = a2
Length of outer side =(a+4) m
Area of outer square=(a+4)2
= a2+8a+16
Area of the path = Area of outer sqare-Area of low
⇒240=a2+8a+16−a2
⇒240=8a+16
⇒8(a+2)=240
⇒a+2=8240
⇒a+2=30
⇒a=30−2
⇒a=28
side of lawn =30 m
Area of lawn = 28×28
= 784 m2
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