The area of a square field is 64 hectares .Find the cost of fencing it with wire at Rs. 21.50 per metre .

Answer

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

### Step 1: Convert the area from hectares to square meters.
The area of the square field is given as 64 hectares. We know that 1 hectare is equal to 10,000 square meters.

\[ \text{Area in square meters} = 64 \text{ hectares} \times 10,000 \text{ m}^2/\text{hectare} = 640,000 \text{ m}^2 \]

### Step 2: Use the area to find the side length of the square.
The formula for the area of a square is given by:

\[ \text{Area} = \text{side}^2 \]

We can rearrange this to find the side length:

\[ \text{side} = \sqrt{\text{Area}} = \sqrt{640,000} \text{ m} \]

Calculating the square root:

\[ \text{side} = 800 \text{ m} \]

### Step 3: Calculate the perimeter of the square.
The perimeter \( P \) of a square can be calculated using the formula:

\[ P = 4 \times \text{side} \]

Substituting the value of the side:

\[ P = 4 \times 800 \text{ m} = 3200 \text{ m} \]

### Step 4: Calculate the cost of fencing.
The cost of fencing is given as Rs. 21.50 per meter. To find the total cost, we multiply the perimeter by the cost per meter:

\[ \text{Total Cost} = \text{Perimeter} \times \text{Cost per meter} = 3200 \text{ m} \times 21.50 \text{ Rs/m} \]

Calculating the total cost:

\[ \text{Total Cost} = 68,800 \text{ Rs} \]

### Final Answer:
The cost of fencing the square field is Rs. 68,800.

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