If the length of a rectangle is increased by `4%` and breadth of the rectangle is decreased by `5%`, find the percentage change in area.

Options

A. `1.2%` increase
B. `0.8%` increase
C. `1.2%` decrease
D. `0.8%` decrease

Answer

To find the percentage change in the area of a rectangle when its length is increased by 4% and its breadth is decreased by 5%, we can follow these steps:

### Step 1: Define the original dimensions
Let the original length of the rectangle be \( L \) and the original breadth be \( B \).

### Step 2: Calculate the new dimensions
- The new length after a 4% increase:
\[ \text{New Length} = L + 0.04L = 1.04L \]

- The new breadth after a 5% decrease:
\[ \text{New Breadth} = B - 0.05B = 0.95B \]

### Step 3: Calculate the original area
The original area \( A \) of the rectangle is given by:
\[ A = L \times B \]

### Step 4: Calculate the new area
The new area \( A' \) after the changes in dimensions is:
\[ A' = \text{New Length} \times \text{New Breadth} = (1.04L) \times (0.95B) \]
\[ A' = 1.04 \times 0.95 \times L \times B \]
\[ A' = 0.988 \times (L \times B) = 0.988A \]

### Step 5: Calculate the percentage change in area
The percentage change in area can be calculated using the formula:
\[ \text{Percentage Change} = \left( \frac{\text{New Area} - \text{Original Area}}{\text{Original Area}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Change} = \left( \frac{0.988A - A}{A} \right) \times 100 \]
\[ \text{Percentage Change} = \left( \frac{-0.012A}{A} \right) \times 100 = -1.2\% \]

### Conclusion
The percentage change in area is \(-1.2\%\), indicating a decrease in the area.

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