It costs Rs. 5400 to fence a square field at Rs. 13.50 per metre . Find (i) the length of the side of the field (ii) the area of the field.

Answer

To solve the problem step by step, we will follow the instructions provided in the video transcript.

### Step 1: Find the Perimeter of the Square Field
First, we need to find the perimeter of the square field. The total cost to fence the field is Rs. 5400, and the cost per meter is Rs. 13.50.

**Formula:**
\[ \text{Perimeter} = \frac{\text{Total Cost}}{\text{Cost per meter}} \]

**Calculation:**
\[ \text{Perimeter} = \frac{5400}{13.50} = 400 \text{ meters} \]

### Step 2: Relate Perimeter to the Side Length
The perimeter of a square is given by the formula:
\[ \text{Perimeter} = 4 \times \text{Side} \]

We can set this equal to the perimeter we calculated:
\[ 4 \times \text{Side} = 400 \]

### Step 3: Solve for the Length of the Side
To find the length of one side of the square, we divide the perimeter by 4:
\[ \text{Side} = \frac{400}{4} = 100 \text{ meters} \]

### Step 4: Calculate the Area of the Square Field
Now that we have the length of the side, we can calculate the area of the square field. The area \(A\) of a square is given by:
\[ A = \text{Side}^2 \]

**Calculation:**
\[ A = 100^2 = 10000 \text{ square meters} \]

### Final Answers
(i) The length of the side of the field is **100 meters**.
(ii) The area of the field is **10,000 square meters**.

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