Question

A square lawn is surrounded by a path 2 m wide. If the area of
the path is 240 m², find the area of the lawn

Answer 1

Length of outer side = (a + 2 + 2) = (a + 4) m. Area of outer side = (a + 4)² = a² + 8a + 16. Also given, Area of path is 240 m².

Answer 2

Answer

Let the side of lawn be 'a' m.

Let the side of lawn be 'a' m.Area of lawn = a2

Let the side of lawn be 'a' m.Area of lawn = a2Length of outer side =(a+4) m

Let the side of lawn be 'a' m.Area of lawn = a2Length of outer side =(a+4) mArea of outer square=(a+4)2

Let the side of lawn be 'a' m.Area of lawn = a2Length of outer side =(a+4) mArea of outer square=(a+4)2= a2+8a+16

Let the side of lawn be 'a' m.Area of lawn = a2Length of outer side =(a+4) mArea of outer square=(a+4)2= a2+8a+16Area of the path = Area of outer sqare-Area of low

Let the side of lawn be 'a' m.Area of lawn = a2Length of outer side =(a+4) mArea of outer square=(a+4)2= a2+8a+16Area of the path = Area of outer sqare-Area of low⇒240=a2+8a+16−a2

Let the side of lawn be 'a' m.Area of lawn = a2Length of outer side =(a+4) mArea of outer square=(a+4)2= a2+8a+16Area of the path = Area of outer sqare-Area of low⇒240=a2+8a+16−a2⇒240=8a+16

Let the side of lawn be 'a' m.Area of lawn = a2Length of outer side =(a+4) mArea of outer square=(a+4)2= a2+8a+16Area of the path = Area of outer sqare-Area of low⇒240=a2+8a+16−a2⇒240=8a+16⇒8(a+2)=240

Let the side of lawn be 'a' m.Area of lawn = a2Length of outer side =(a+4) mArea of outer square=(a+4)2= a2+8a+16Area 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+2=30⇒a=30−2

⇒a+2=30⇒a=30−2⇒a=28

⇒a+2=30⇒a=30−2⇒a=28side of lawn =30 m

⇒a+2=30⇒a=30−2⇒a=28side of lawn =30 mArea of lawn = 28×28

⇒a+2=30⇒a=30−2⇒a=28side of lawn =30 mArea of lawn = 28×28                      = 784 m2