A square lawn has a 2m wide path surrounding it. If the area of the path is 136 square m, find the area of the lawn.Please give the ans with detailed steps.

Let the length of path be a m.

Total area

Area of lawn = Total area – Area of path

 

Area of lawn

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length of the path (BC) = a metre

length of the side of the lawn (FG) = (a - 4)m

Area of the path =136 m2

Area of the lawn=Total area (a2) - Area of path

(a - 4)2 = a2 - 136

(a - 4)2  _ a= -136

a2 -8a + 16  - a2 = -136  (a - b)2  = a2 - 2ab +b2

-8a + 16 = -136

- 8a = - 136-16

  = - 152

a = - 152/ -8

  a = 19

length of  side of lawn  = a - 4 

  = 19 - 4  = 15m

Area of the lawn  =  152 

  =  225 m2

   

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