If the length of a rectangle is increased by `5 %` and the breadth of the rectangle is decreased by `6 %`, then find the percentage change in area.

Answer

To solve the problem of finding the percentage change in the area of a rectangle when its length is increased by 5% and its breadth is decreased by 6%, 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 5% increase can be calculated as:
\[ \text{New Length} = L + 0.05L = 1.05L \]

- The new breadth after a 6% decrease can be calculated as:
\[ \text{New Breadth} = B - 0.06B = 0.94B \]

### 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:
\[ A' = \text{New Length} \times \text{New Breadth} = (1.05L) \times (0.94B) \]
Calculating this gives:
\[ A' = 1.05 \times 0.94 \times L \times B = 0.987 \times (L \times B) \]

### Step 5: Calculate the percentage change in area
The percentage change in area can be calculated using the formula:
\[ \text{Percentage Change} = \left( \frac{A' - A}{A} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Change} = \left( \frac{0.987LB - LB}{LB} \right) \times 100 = \left( \frac{-0.013LB}{LB} \right) \times 100 = -1.3\% \]

### Conclusion
The percentage change in the area of the rectangle is \(-1.3\%\).

---