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

Options

A. 0.22
B. 0.24
C. 0.2
D. 0.2096

Answer

To solve the problem step by step, we will calculate the increase in area of the rectangle when its length and breadth are increased by 8% and 12% respectively.

### Step 1: Define the original dimensions
Let the original length (L) of the rectangle be 100 units and the original breadth (B) be 100 units.

### Step 2: Calculate the new dimensions after the increase
- The new length after an 8% increase:
\[ \text{New Length} = L + (8\% \text{ of } L) = 100 + (0.08 \times 100) = 100 + 8 = 108 \text{ units} \]

- The new breadth after a 12% increase:
\[ \text{New Breadth} = B + (12\% \text{ of } B) = 100 + (0.12 \times 100) = 100 + 12 = 112 \text{ units} \]

### Step 3: Calculate the original area
The original area (A) of the rectangle is given by:
\[ \text{Original Area} = L \times B = 100 \times 100 = 10,000 \text{ square units} \]

### Step 4: Calculate the new area
The new area (A') after the increases in dimensions is:
\[ \text{New Area} = \text{New Length} \times \text{New Breadth} = 108 \times 112 \]
Calculating this gives:
\[ \text{New Area} = 108 \times 112 = 12,096 \text{ square units} \]

### Step 5: Calculate the increase in area
The increase in area (ΔA) is:
\[ \Delta A = \text{New Area} - \text{Original Area} = 12,096 - 10,000 = 2,096 \text{ square units} \]

### Step 6: Calculate the percentage increase in area
The percentage increase in area is calculated as:
\[ \text{Percentage Increase} = \left( \frac{\Delta A}{\text{Original Area}} \right) \times 100 = \left( \frac{2,096}{10,000} \right) \times 100 \]
Calculating this gives:
\[ \text{Percentage Increase} = 20.96\% \]

### Step 7: Final answer
Since the options do not include decimals, we can express this as:
\[ \text{Percentage Increase} = 20.96\% \approx 21\% \]