Question

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

Answer 1

Step-by-step explanation:

Let the side of lawn be 'a' m.

Area of lawn = a

2

Length of outer side =(a+4) m

Area of outer square=(a+4)

2

= a

2

+8a+16

Area of the path = Area of outer sqare-Area of low

⇒240=a

2

+8a+16−a

2

⇒240=8a+16

⇒8(a+2)=240

⇒a+2=

8

240

⇒a+2=30

⇒a=30−2

⇒a=28

side of lawn =30 m

Area of lawn = 28×28

= 784

$m {}^{2}$