Question

a square lawn is surrounded by a path. if the are of the path is 165m^2,find the cost of levelling the path at rupees 20 per m square ​

Answer 1

Answer:

Consider the side of the lawn be x

Given width of the path 2.5m

Side of the lawn including path x+2(2.5)=x+5

Area of a square  =(side)  

2

 

So, area of lawn = (Area of the lawn including the path) - (Area of the path)

Therefore, According to the given question,:

 x  

2

=(x + 5)  

2

−165

  x  

2

=(x  

2

 + 10x +25)−165m  

2

 

  x  

2

=x  

2

+10x+25−165

  x  

2

=x  

2

 +10x−140

  x  

2

 −140=x  

2

−10x

  x  

2

−x  

2

−140=−10x

 −140=−10x

 i.e 140=10x

  ∴x=140/10=14

Since the side of the lawn = 14m

The area of the lawn=(14)  

2

or196 m  

2

 .

Answer 2

Step-by-step explanation:

$consider \: the \: side \: of \: the \: lawn \: be \: = x \\ given \: width \: of \: the \: path \: = 2.5m \\ side \: of \: the \: lawn \: including \: path \: = x + 2(2.5) = x + 5 \\ area \: of \: a \: square \: = (side) {}^{2} \\ so \: area \: of \: lawn \: = area \: of \: the \: lawn \: including \: the \: path - area \: of \: the \: path \\ therefore \: according \: to \: the \: question \\ {x}^{2} = {x + 5}^{2} - 165 \\ {x }^{2} = ( {x}^{2} + 10x \: + 25) - {165m}^{2} \\ {x}^{2} = { x}^{2} + 10x + 25 - 165 \\ {x}^{2} = {x}^{2} + 10x - 140 \\ {x}^{2} - 140 = {x}^{2} - 10x \\ {x}^{2} - {x}^{2} - 140 = - 10x \\ - 140 = - 10x \\ i.e \: 140 = 10x \\ therefore \: x \: = \frac{140}{10} = 14 \\ since \: the \: side \: of \: the \: lawn \: = 14m \\ the \: area \: of \: the \: lawn \: = {14}^{2} or \: 196 {m}^{2}$