On increasing the length of a reactangle by 20% and decreasing its breadth by 20 % what is the change in its area ?

Options

A. 20% increase
B. 20% decrease
C. No change
D. 4% decrease

Explanation

To solve the problem of finding the change in area when the length of a rectangle is increased by 20% and the breadth is decreased by 20%, 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 Original Area:**
The original area \( A \) of the rectangle is given by the formula:
\[ A = L \times B \]

3. **Calculate the New Length:**
The length is increased by 20%. Therefore, the new length \( L' \) can be calculated as:
\[ L' = L + 0.20L = 1.20L = \frac{120}{100}L = \frac{6}{5}L \]

4. **Calculate the New Breadth:**
The breadth is decreased by 20%. Therefore, the new breadth \( B' \) can be calculated as:
\[ B' = B - 0.20B = 0.80B = \frac{80}{100}B = \frac{4}{5}B \]

5. **Calculate the New Area:**
The new area \( A' \) of the rectangle with the new dimensions is:
\[ A' = L' \times B' = \left(\frac{6}{5}L\right) \times \left(\frac{4}{5}B\right) = \frac{24}{25}LB \]

6. **Determine the Change in Area:**
The change in area can be calculated by finding the difference between the original area and the new area:
\[ \text{Change in Area} = A - A' = LB - \frac{24}{25}LB = \left(1 - \frac{24}{25}\right)LB = \frac{1}{25}LB \]

7. **Calculate the Percentage Change in Area:**
To find the percentage change in area, we use the formula:
\[ \text{Percentage Change} = \left(\frac{\text{Change in Area}}{\text{Original Area}}\right) \times 100 = \left(\frac{\frac{1}{25}LB}{LB}\right) \times 100 = \frac{1}{25} \times 100 = 4\% \]

### Final Answer:
The area of the rectangle decreases by **4%**.