The cost of fencing a rectangular field at Rs 24 per metre is Rs 1980. if its length is 23 m. find its breadth.

Options

A. 27.25 m.
B. 14 m
C. 18.25 m
D. 10 m

Answer

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

### Step 1: Understand the problem
We need to find the breadth of a rectangular field given its length and the total cost of fencing.

### Step 2: Identify the given information
- Length of the rectangular field (L) = 23 meters
- Cost of fencing per meter = Rs. 24
- Total cost of fencing = Rs. 1980

### Step 3: Calculate the perimeter of the rectangular field
The cost of fencing is calculated based on the perimeter of the field. The formula for the perimeter (P) of a rectangle is:
\[ P = 2 \times (L + B) \]
Where L is the length and B is the breadth.

First, we need to find the total perimeter using the total cost and cost per meter:
\[ \text{Total Perimeter} = \frac{\text{Total Cost}}{\text{Cost per meter}} \]
\[ \text{Total Perimeter} = \frac{1980}{24} \]

### Step 4: Perform the division
\[ \text{Total Perimeter} = 82.5 \text{ meters} \]

### Step 5: Set up the equation for perimeter
Now we can set up the equation using the perimeter formula:
\[ 2 \times (23 + B) = 82.5 \]

### Step 6: Simplify the equation
Divide both sides by 2:
\[ 23 + B = \frac{82.5}{2} \]
\[ 23 + B = 41.25 \]

### Step 7: Solve for B (breadth)
Now, isolate B:
\[ B = 41.25 - 23 \]
\[ B = 18.25 \text{ meters} \]

### Conclusion
The breadth of the rectangular field is 18.25 meters.

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