Question

О.
· A Square lawn is Surrounded by a
path
6m wide around it. If the area
of the path is 360 sq; m. find the area
of the lawn.​

Answer 1

Answer:

The required area of the lawn is 81 m²

Step-by-step explanation:

Given :

• A square lawn is surrounded by a path 6 m wide around it.

• The area of the path is 360 m²

To find :

the area of the lawn

Solution :

Let the side of the square lawn be 'x' m

Area of the square lawn :

side = x

➙ Area = (side)²

➙ Area = x²

∴ The area of the square lawn is x²

Area of the path = 360 m²

width of the path = 6 m

Side of the lawn including path = x + 2(6) = 12 + x

Area of the lawn including path :

side = (12 + x)

➙ Area = (12 + x)²

➙ Area = 12² + x² + 2(12)(x)

➙ Area = 144 + x² + 24x

Area of the lawn including path = Area of the square lawn + Area of the path

144 + x² + 24x = x² + 360

144 + 24x = 360

 24x = 360 - 144

 24x = 216

   x = 216/24

  x = 9

Therefore, the side of the square lawn is 9 m

Area of the lawn :

side = 9 m

➙ Area = (side)²

➙ Area = 9²

➙ Area = 81 m²

∴ The area of the lawn is 81 m²