A garden in form of a square is surrounded by a path which is 1m wide on two opposite sides and 1^2m wide on the other two opposite sides.if the area of the path is 17m^2.Calculate the perimeter of the garden and the area of the space covered by the garden and the paths
I suspect a typo, as 1m is the same as 1^2 m
Perimeter of the garden is 20m and area of the space covered by the garden and the path is 42m^2
Agraden20 m long and 17m wide is surrounded by a path 2mwide find the area of the path
To solve this problem, let's break it down step by step:
Step 1: Visualize the problem
First, let's understand the given information and visualize the problem. We have a garden in the shape of a square, and it is surrounded by a path. The width of the path on two opposite sides is 1 meter, and on the other two opposite sides, it is 1^2 square meters. We also know that the area of the path is 17 square meters.
Step 2: Calculate the dimensions of the garden
Let's assume the side length of the garden (square) is x meters. Since the path surrounds the garden on four sides, the dimensions of the garden can be calculated as follows:
- Length of the garden (including the paths) = x + 2 (1-meter paths) + 2 (1^2-square-meter paths) = x + 2 + 2 = x + 4
- Width of the garden (including the paths) = x + 2 (1-meter paths) = x + 2
Step 3: Calculate the area of the garden
The area of the garden can be calculated by multiplying the length and width. Since the garden is square, the length and width are the same:
- Area of the garden (including the paths) = (Length of the garden) * (Width of the garden) = (x + 4) * (x + 2)
Step 4: Calculate the area of the path
The area of the path can be calculated by subtracting the area of the garden from the total area of the garden and paths (which is given as 17 square meters):
- Area of the path = Total area of garden and paths - Area of the garden = 17 - (x + 4) * (x + 2)
Step 5: Solve for x
Now we can solve the equation to find the value of x. We know that the area of the path is 17 square meters:
- Area of the path = 17 = (x + 4) * (x + 2)
Step 6: Calculate the perimeter of the garden
Since we now know the value of x, we can calculate the perimeter of the garden by adding the lengths of all four sides of the garden:
- Perimeter of the garden = 4 * (Length of the garden) = 4 * (x)
Step 7: Calculate the area of the garden and paths
Lastly, we can calculate the total area of the garden and paths by adding the area of the garden and the area of the path:
- Area of the garden and paths = Area of the garden + Area of the path
By following these steps, you can calculate the perimeter of the garden and the area of the space covered by the garden and paths.