Cost of gardening the circular field C at Rs.10 per meter square is Rs.3465. Side of the square field S is equals to the diameter of the circular field C. find the perimeter of square field.

Options

A. 108
B. 84 m
C. 78 m
D. 112 m

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Understand the Cost of Gardening
The cost of gardening the circular field is given as Rs. 3465, and the rate is Rs. 10 per square meter.

### Step 2: Calculate the Area of the Circular Field
To find the area of the circular field, we can use the formula:
\[ \text{Area} = \frac{\text{Total Cost}}{\text{Rate}} = \frac{3465}{10} = 346.5 \text{ m}^2 \]

### Step 3: Use the Area Formula for a Circle
The area of a circle is given by the formula:
\[ \text{Area} = \pi r^2 \]
We can use \(\pi \approx \frac{22}{7}\). Setting the area equal to the area we calculated:
\[ \frac{22}{7} r^2 = 346.5 \]

### Step 4: Solve for \(r^2\)
To isolate \(r^2\), multiply both sides by \(\frac{7}{22}\):
\[ r^2 = 346.5 \times \frac{7}{22} \]
Calculating the right side:
\[ r^2 = 346.5 \times \frac{7}{22} = 346.5 \times 0.31818 \approx 110.0 \]

### Step 5: Find the Radius \(r\)
Now, take the square root to find \(r\):
\[ r = \sqrt{110} \approx 10.49 \text{ m} \]

### Step 6: Calculate the Diameter of the Circular Field
The diameter \(d\) of the circular field is:
\[ d = 2r \approx 2 \times 10.49 \approx 20.98 \text{ m} \]

### Step 7: Determine the Side of the Square Field
The side \(S\) of the square field is equal to the diameter of the circular field:
\[ S = d \approx 20.98 \text{ m} \]

### Step 8: Calculate the Perimeter of the Square Field
The perimeter \(P\) of a square is given by:
\[ P = 4 \times S \]
Substituting the value of \(S\):
\[ P = 4 \times 20.98 \approx 83.92 \text{ m} \]

### Final Answer
The perimeter of the square field is approximately **84 meters**.

---