A cost of cultivating a square field at a rate of rs 135 per hectare is rs 1215. The cost of putting a fence around it at the rate of 75 paise per metre would be

Options

A. `? 360`
B. `? 810`
C. `? 900`
D. `? 1800`

Answer

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

### Step 1: Calculate the area of the square field
The cost of cultivating the square field is given as Rs 1215 at the rate of Rs 135 per hectare.

To find the area in hectares, we use the formula:
\[ \text{Area (hectares)} = \frac{\text{Total Cost}}{\text{Cost per hectare}} = \frac{1215}{135} \]

Calculating this gives:
\[ \text{Area (hectares)} = 9 \text{ hectares} \]

### Step 2: Convert area from hectares to square meters
Since 1 hectare is equal to 10,000 square meters, we convert the area:
\[ \text{Area (m}^2\text{)} = 9 \text{ hectares} \times 10,000 \text{ m}^2/\text{hectare} = 90,000 \text{ m}^2 \]

### Step 3: Find the side length of the square field
For a square field, the area is given by:
\[ \text{Area} = \text{side}^2 \]
Thus, to find the side length, we take the square root of the area:
\[ \text{side} = \sqrt{90,000} \approx 300 \text{ m} \]

### Step 4: Calculate the perimeter of the square field
The perimeter \( P \) of a square is given by:
\[ P = 4 \times \text{side} \]
Substituting the side length:
\[ P = 4 \times 300 = 1200 \text{ m} \]

### Step 5: Calculate the cost of putting a fence around the field
The cost of putting a fence is given as Rs 0.75 (75 paise) per meter. Therefore, the total cost \( C \) for fencing is:
\[ C = \text{Perimeter} \times \text{Cost per meter} = 1200 \text{ m} \times 0.75 \text{ Rs/m} \]
Calculating this gives:
\[ C = 1200 \times 0.75 = 900 \text{ Rs} \]

### Final Answer
The cost of putting a fence around the square field is Rs 900.

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