If the length and breadth of a rectangle are increased by `10 %` and `8 %` ,respectively, then by what per cent will the area of that rectangle be increased?

Answer

To find the percentage increase in the area of a rectangle when its length and breadth are increased by 10% and 8% respectively, 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 original area
The original area \( A \) of the rectangle is given by the formula:
\[ A = L \times B \]

### Step 3: Calculate the new dimensions
- The new length after a 10% increase is:
\[ L' = L + 0.10L = 1.10L \]
- The new breadth after an 8% increase is:
\[ B' = B + 0.08B = 1.08B \]

### Step 4: Calculate the new area
The new area \( A' \) of the rectangle with the increased dimensions is:
\[ A' = L' \times B' = (1.10L) \times (1.08B) \]
\[ A' = 1.10 \times 1.08 \times L \times B \]
\[ A' = 1.188L \times B \]

### Step 5: Calculate the increase in area
The increase in area \( \Delta A \) is given by:
\[ \Delta A = A' - A = (1.188L \times B) - (L \times B) \]
\[ \Delta A = (1.188 - 1) \times L \times B \]
\[ \Delta A = 0.188L \times B \]

### Step 6: Calculate the percentage increase in area
The percentage increase in area is given by:
\[ \text{Percentage Increase} = \left( \frac{\Delta A}{A} \right) \times 100 \]
\[ \text{Percentage Increase} = \left( \frac{0.188L \times B}{L \times B} \right) \times 100 \]
\[ \text{Percentage Increase} = 0.188 \times 100 = 18.8\% \]

Thus, the area of the rectangle will increase by **18.8%**.