A street of width 10 metres surrounds from outside a rectangular garden whose measurement is `200m xx 180 m`. The area of the path (in square metres) is

Options

A. 8000
B. 7000
C. 7500
D. 8200

Answer

To find the area of the path surrounding the rectangular garden, we will follow these steps:

### Step 1: Calculate the dimensions of the outer rectangle
The garden has dimensions of 200 meters (length) and 180 meters (width). Since the path surrounding the garden is 10 meters wide on all sides, we need to add twice the width of the path (10 meters on each side) to both the length and the width of the garden.

- **Outer Length** = Garden Length + 2 × Path Width
= 200 m + 2 × 10 m
= 200 m + 20 m
= 220 m

- **Outer Width** = Garden Width + 2 × Path Width
= 180 m + 2 × 10 m
= 180 m + 20 m
= 200 m

### Step 2: Calculate the area of the outer rectangle
Now, we will calculate the area of the outer rectangle (which includes the garden and the path).

- **Area of Outer Rectangle** = Outer Length × Outer Width
= 220 m × 200 m
= 44000 m²

### Step 3: Calculate the area of the inner rectangle (the garden)
Next, we calculate the area of the inner rectangle, which is the garden itself.

- **Area of Inner Rectangle** = Garden Length × Garden Width
= 200 m × 180 m
= 36000 m²

### Step 4: Calculate the area of the path
Finally, we find the area of the path by subtracting the area of the inner rectangle from the area of the outer rectangle.

- **Area of Path** = Area of Outer Rectangle - Area of Inner Rectangle
= 44000 m² - 36000 m²
= 8000 m²

### Final Answer
The area of the path surrounding the garden is **8000 square meters**.

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