Cost of fencing around a square field is Rs. 12000. If the cost of fencing per metre is Rs. 30, find the area of the square field.

Answer

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

### Step 1: Understand the given information
We know the total cost of fencing around the square field is Rs. 12,000 and the cost of fencing per meter is Rs. 30.

### Step 2: Calculate the perimeter of the square field
To find the perimeter, we can use the formula:
\[ \text{Perimeter} = \frac{\text{Total Cost}}{\text{Cost per meter}} \]

Substituting the values:
\[ \text{Perimeter} = \frac{12000}{30} \]

### Step 3: Perform the division
Now, we calculate:
\[ \text{Perimeter} = 400 \text{ meters} \]

### Step 4: Relate perimeter to the side of the square
The perimeter of a square is given by the formula:
\[ \text{Perimeter} = 4 \times \text{Side} \]

Let’s denote the side of the square as \( s \). Therefore, we can write:
\[ 4s = 400 \]

### Step 5: Solve for the side of the square
To find the side, we divide both sides of the equation by 4:
\[ s = \frac{400}{4} \]

Calculating this gives:
\[ s = 100 \text{ meters} \]

### Step 6: Calculate the area of the square field
The area \( A \) of a square is given by:
\[ A = \text{Side} \times \text{Side} = s \times s \]

Substituting the value of \( s \):
\[ A = 100 \times 100 \]

### Step 7: Perform the multiplication
Calculating this gives:
\[ A = 10000 \text{ square meters} \]

### Final Answer
The area of the square field is **10,000 square meters**.

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