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.
Answers
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