There is a rectangular garden of dimensions 480 metre `xx` 160 metre. A path of width 3 metre is built outside the garden. What is the area (in `"metre"^(2)`) of the path ?

Options

A. 3984
B. 1892
C. 2796
D. 3876

Answer

To find the area of the path built outside the rectangular garden, we can follow these steps:

### Step 1: Determine the dimensions of the garden.
The dimensions of the rectangular garden are given as:
- Length = 480 meters
- Width = 160 meters

### Step 2: Calculate the dimensions of the outer rectangle (garden + path).
Since the path is 3 meters wide on all sides, we need to add twice the width of the path to each dimension of the garden (once for each side).

- New Length = 480 meters + 2 × 3 meters = 480 + 6 = 486 meters
- New Width = 160 meters + 2 × 3 meters = 160 + 6 = 166 meters

### Step 3: Calculate the area of the outer rectangle.
Area of the outer rectangle (garden + path) can be calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]

Substituting the values:
\[ \text{Area}_{\text{outer}} = 486 \, \text{meters} \times 166 \, \text{meters} \]

Calculating this gives:
\[ \text{Area}_{\text{outer}} = 80676 \, \text{m}^2 \]

### Step 4: Calculate the area of the inner rectangle (garden only).
Area of the inner rectangle (garden) can be calculated using the same formula:
\[ \text{Area}_{\text{inner}} = 480 \, \text{meters} \times 160 \, \text{meters} \]

Calculating this gives:
\[ \text{Area}_{\text{inner}} = 76800 \, \text{m}^2 \]

### Step 5: Calculate the area of the path.
The area of the path is the difference between the area of the outer rectangle and the area of the inner rectangle:
\[ \text{Area}_{\text{path}} = \text{Area}_{\text{outer}} - \text{Area}_{\text{inner}} \]

Substituting the values:
\[ \text{Area}_{\text{path}} = 80676 \, \text{m}^2 - 76800 \, \text{m}^2 \]
\[ \text{Area}_{\text{path}} = 3876 \, \text{m}^2 \]

### Final Answer:
The area of the path is **3876 square meters**.

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