What will be the cost of fencing a rectangular plot ? A. Cost of fencing rectangular plot whose area is `316m^(2)` is Rs.968. B. Perimeter of the rectangular plot is 200 m. C. Perimeter of the square whose length is equal to the breadth of the rectangular plot is 20 m.

Options

A. Only C
B. A and C together
C. A and B together
D. A and either B or C

Explanation

To determine the cost of fencing a rectangular plot based on the given statements, we need to analyze each statement carefully.

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to find the cost of fencing a rectangular plot. We have three statements that provide information about the area, perimeter, and cost.

2. **Analyzing Statement A**:
- Statement A states that the cost of fencing a rectangular plot whose area is 316 m² is Rs. 968.
- This gives us the cost per square meter of area but does not directly help us find the perimeter or the dimensions of the rectangular plot.

3. **Analyzing Statement B**:
- Statement B states that the perimeter of the rectangular plot is 200 m.
- The perimeter (P) of a rectangle is given by the formula:
\[ P = 2 \times (length + breadth) \]
- This information is crucial as it allows us to establish a relationship between the length and breadth of the rectangle.

4. **Analyzing Statement C**:
- Statement C states that the perimeter of a square whose length is equal to the breadth of the rectangular plot is 20 m.
- The perimeter of a square (P) is given by the formula:
\[ P = 4 \times side \]
- From this, we can find that the side of the square is:
\[ side = \frac{20}{4} = 5 m \]
- Therefore, if the breadth of the rectangular plot is equal to the side of the square, the breadth is 5 m.

5. **Finding Length of the Rectangle**:
- Now, we can use the perimeter of the rectangular plot (200 m) to find the length.
- Let the breadth (b) = 5 m.
- Using the perimeter formula:
\[ 200 = 2 \times (length + breadth) \]
\[ 200 = 2 \times (length + 5) \]
\[ 100 = length + 5 \]
\[ length = 100 - 5 = 95 m \]

6. **Calculating the Area**:
- Now, we can calculate the area of the rectangular plot:
\[ Area = length \times breadth = 95 \times 5 = 475 m² \]
- However, we already know from Statement A that the area is 316 m², which indicates that the dimensions we calculated do not match the area given in Statement A.

7. **Conclusion**:
- Since the area calculated does not match the area given in Statement A, we cannot determine the cost of fencing based solely on the statements provided.
- To find the cost of fencing, we need to know the cost per meter of fencing, which is not provided in any of the statements.

### Final Answer:
Based on the analysis, we cannot definitively determine the cost of fencing the rectangular plot with the information given.