Question

A square lawn is surrounded by a path 2.5 m wide . if the area of the path is 165 m, find the area of the lawn​

Answer 1

Answer:

Step-by-step explanation:

Area = 165 m^2  

2

 

Width = 2.5 m

Let side of square lawn = x m

Outer side = x + 2 x 2.5

= (x + 5) m

Area of path = \left(x+5\right)^2-x^2(x+5)  

2

−x  

2

 

x^2+10x+25-x^2=165x  

2

+10x+25−x  

2

=165

10x = 165 - 25 = 140

x=\frac{140}{10}=14\ mx=  

10

140

​  

=14 m

Side of lawn = 14 m

Area of lawn = 14 x 14 = 196 m^2  

2

Answer 2

Step-by-step explanation:

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》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,:

  》x²=(x + 5)²−165

  》 x²=(x² + 10x +25)−165m²

 》  x²=x²+10x+25−165

》   x²=x² +10x−140

》   x² −140=x2−10x

 》  x²−x²−140=−10x

  》−140=−10x

》  i.e 140=10x

  》 ∴x=140/10=14

》Since the side of the lawn = 14m

》The area of the lawn=(14)²or196 m² .