The length and breadth of a rectangular fields are 120 m and 80 m respectively . Inside the field , a path of 12 m width is made around the field. The area of the path is :

Options

A. `2358 m^(2) `
B. `7344 m^(2) `
C. `4224 m^(2) `
D. `3224 m^(2) `

Answer

To find the area of the path around the rectangular field, we will follow these steps:

### Step 1: Calculate the dimensions of the outer rectangle.
The original dimensions of the rectangular field are:
- Length = 120 m
- Breadth = 80 m

Since there is a path of width 12 m around the field, we need to add twice the width of the path to both the length and the breadth (12 m on each side).

**Outer Length = Length of the field + 2 × Width of the path**
\[ \text{Outer Length} = 120 + 2 \times 12 = 120 + 24 = 144 \text{ m} \]

**Outer Breadth = Breadth of the field + 2 × Width of the path**
\[ \text{Outer Breadth} = 80 + 2 \times 12 = 80 + 24 = 104 \text{ m} \]

### Step 2: Calculate the area of the outer rectangle.
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]

Using the outer dimensions:
\[ \text{Area of the outer rectangle} = 144 \times 104 \]
Calculating this gives:
\[ \text{Area of the outer rectangle} = 14976 \text{ m}^2 \]

### Step 3: Calculate the area of the inner rectangle (the field).
Using the original dimensions of the field:
\[ \text{Area of the inner rectangle} = 120 \times 80 \]
Calculating this gives:
\[ \text{Area of the inner rectangle} = 9600 \text{ m}^2 \]

### Step 4: 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:
\[ \text{Area of the path} = \text{Area of the outer rectangle} - \text{Area of the inner rectangle} \]
Substituting the values:
\[ \text{Area of the path} = 14976 - 9600 = 5366 \text{ m}^2 \]

### Conclusion
The area of the path is **5366 m²**.

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