If the longer side of a rectangle is doubled and the other is reduced to half, then the area of the new rectangle goes up by :

Options

A. `50% `
B. `100% `
C. `0% `
D. `150%`

Answer

To solve the problem step by step, we will follow the given scenario of changing the dimensions of a rectangle and calculating the area increment.

### Step-by-Step Solution:

1. **Define the Dimensions of the Rectangle:**
Let the longer side of the rectangle be \( L \) and the shorter side be \( B \).

2. **Calculate the Area of the Original Rectangle:**
The area \( A \) of the original rectangle can be calculated using the formula:
\[ A = L \times B \]

3. **Change the Dimensions:**
According to the problem:
- The longer side is doubled: New length = \( 2L \)
- The shorter side is reduced to half: New breadth = \( \frac{B}{2} \)

4. **Calculate the Area of the New Rectangle:**
The area \( A' \) of the new rectangle can be calculated as:
\[ A' = (2L) \times \left(\frac{B}{2}\right) \]
Simplifying this gives:
\[ A' = 2L \times \frac{B}{2} = L \times B = A \]

5. **Calculate the Change in Area:**
The change in area can be calculated as:
\[ \text{Change in Area} = A' - A = A - A = 0 \]

6. **Calculate the Percentage Increase in Area:**
To find the percentage increase in area, we use the formula:
\[ \text{Percentage Increase} = \left(\frac{\text{Change in Area}}{\text{Original Area}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage Increase} = \left(\frac{0}{A}\right) \times 100 = 0\% \]

### Final Answer:
The area of the new rectangle goes up by **0%**.