The length and breadth of a rectangular field are in the ratio `3:2`. If the area of the field is `3456 m^(2)` .Find the cost of fencing it at Rs. 60 per m.

Options

A. Rs. 4400
B. Rs. 10000
C. Rs. 14000
D. Rs. 14400

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Understand the Ratio of Length and Breadth
The length (L) and breadth (B) of the rectangular field are in the ratio of 3:2. We can represent this as:
- Length = 3x
- Breadth = 2x

### Step 2: Write the Area Formula
The area (A) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]
Given that the area of the field is 3456 m², we can write:
\[ 3x \times 2x = 3456 \]

### Step 3: Simplify the Equation
Now, we can simplify the equation:
\[ 6x^2 = 3456 \]

### Step 4: Solve for x²
To find \( x^2 \), divide both sides by 6:
\[ x^2 = \frac{3456}{6} \]
Calculating this gives:
\[ x^2 = 576 \]

### Step 5: Find the Value of x
Now, take the square root of both sides to find x:
\[ x = \sqrt{576} \]
Calculating the square root gives:
\[ x = 24 \, \text{m} \]

### Step 6: Calculate Length and Breadth
Now that we have the value of x, we can find the length and breadth:
- Length \( L = 3x = 3 \times 24 = 72 \, \text{m} \)
- Breadth \( B = 2x = 2 \times 24 = 48 \, \text{m} \)

### Step 7: Calculate the Perimeter
The perimeter (P) of a rectangle is given by the formula:
\[ P = 2 \times (L + B) \]
Substituting the values of L and B:
\[ P = 2 \times (72 + 48) \]
Calculating this gives:
\[ P = 2 \times 120 = 240 \, \text{m} \]

### Step 8: Calculate the Cost of Fencing
The cost of fencing is given at Rs. 60 per meter. Therefore, the total cost (C) can be calculated as:
\[ C = \text{Cost per meter} \times \text{Perimeter} \]
Substituting the values:
\[ C = 60 \times 240 \]
Calculating this gives:
\[ C = 14400 \, \text{Rs} \]

### Final Answer
The cost of fencing the rectangular field is Rs. 14400.

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