The cost of enclosing a rectangular garden with a fence all round, at the rate of 75 paise per metre, is Rs 300. If the length of the garden is 120 metres, find the area of the field in square metres.

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the given information
- The cost of enclosing the garden is Rs 300.
- The rate of fencing is 75 paise per metre (which is equivalent to Rs 0.75 per metre).
- The length of the garden is 120 metres.

### Step 2: Calculate the total perimeter of the garden
We know that the total cost of the fencing can be calculated using the formula:
\[ \text{Total Cost} = \text{Rate} \times \text{Perimeter} \]
Rearranging this, we can find the perimeter:
\[ \text{Perimeter} = \frac{\text{Total Cost}}{\text{Rate}} = \frac{300}{0.75} \]

### Step 3: Perform the calculation
Calculating the perimeter:
\[ \text{Perimeter} = \frac{300}{0.75} = 400 \text{ metres} \]

### Step 4: Use the perimeter to find the breadth
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (L + B) \]
Where \( L \) is the length and \( B \) is the breadth. We can rearrange this to find the breadth:
\[ 400 = 2 \times (120 + B) \]
Dividing both sides by 2:
\[ 200 = 120 + B \]
Now, solving for \( B \):
\[ B = 200 - 120 = 80 \text{ metres} \]

### Step 5: Calculate the area of the garden
The area \( A \) of a rectangle is given by:
\[ A = L \times B \]
Substituting the values we have:
\[ A = 120 \times 80 \]

### Step 6: Perform the final calculation
Calculating the area:
\[ A = 9600 \text{ square metres} \]

### Final Answer
The area of the field is **9600 square metres**.

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