If the length and breadth of a rectangle are increased by 8% and 12% respectively, then by what percentage area of that rectangle increase?

Options

A. 22
B. 24
C. 20
D. 20.96

Answer

To solve the problem of how much the area of a rectangle increases when the length and breadth are increased by 8% and 12% respectively, we can follow these steps:

### Step-by-Step Solution:

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

2. **Calculate the New Dimensions**:
- The new length after an 8% increase will be:
\[ L' = L + 0.08L = 1.08L \]
- The new breadth after a 12% increase will be:
\[ B' = B + 0.12B = 1.12B \]

3. **Calculate the Original Area**:
The original area \( A \) of the rectangle is given by:
\[ A = L \times B \]

4. **Calculate the New Area**:
The new area \( A' \) after the increases is:
\[ A' = L' \times B' = (1.08L) \times (1.12B) \]
\[ A' = 1.08 \times 1.12 \times L \times B \]

5. **Calculate the Increase in Area**:
We need to find the percentage increase in area. First, calculate \( 1.08 \times 1.12 \):
\[ 1.08 \times 1.12 = 1.2096 \]
Thus, the new area can be expressed as:
\[ A' = 1.2096 \times A \]

6. **Find the Increase in Area**:
The increase in area is:
\[ \text{Increase} = A' - A = 1.2096A - A = 0.2096A \]

7. **Calculate the Percentage Increase**:
The percentage increase in area is given by:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase}}{A} \right) \times 100 = \left( \frac{0.2096A}{A} \right) \times 100 = 20.96\% \]

### Final Answer:
The area of the rectangle increases by **20.96%**.