If length and breadth of a rectangle became half and double respectively, then what will be the resultant area?

Options

A. `25%`
B. `55%`
C. `75%`
D. None of the above

Answer

To solve the problem step by step, we will analyze the changes in the dimensions of the rectangle and calculate the resultant area.

### Step-by-Step Solution:

1. **Understand the Original Dimensions**:
- Let the original length of the rectangle be \( L \).
- Let the original breadth of the rectangle be \( B \).

2. **Calculate the Original Area**:
- The area \( A \) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} = L \times B \]

3. **Determine the New Dimensions**:
- According to the problem, the length becomes half:
\[ \text{New Length} = \frac{L}{2} \]
- The breadth becomes double:
\[ \text{New Breadth} = 2B \]

4. **Calculate the New Area**:
- The new area \( A' \) can be calculated using the new dimensions:
\[ A' = \text{New Length} \times \text{New Breadth} = \left(\frac{L}{2}\right) \times (2B) \]

5. **Simplify the New Area**:
- Now, simplifying the expression for the new area:
\[ A' = \frac{L}{2} \times 2B = \frac{L \times 2B}{2} = L \times B \]

6. **Compare the Areas**:
- We find that the new area \( A' \) is equal to the original area \( A \):
\[ A' = L \times B = A \]

7. **Conclusion**:
- Therefore, the resultant area remains unchanged. The answer is that there is no change in the area.

### Final Answer:
The resultant area remains the same as the original area.