The length and breadth of square are increased by `30%` and `20%` respectively. The area of the rectangle so formed exceeds the area of the square by-

Options

A. `20%`
B. `36%`
C. `50%`
D. `56%`

Answer

To solve the problem step by step, we will calculate the increase in the area of the rectangle formed by increasing the length and breadth of a square by 30% and 20% respectively.

### Step 1: Define the original dimensions of the square.
Let the side length of the square be \( s \).

### Step 2: Calculate the area of the square.
The area \( A_{square} \) of the square is given by:
\[ A_{square} = s^2 \]

### Step 3: Calculate the new dimensions of the rectangle.
- The length of the rectangle after a 30% increase is:
\[ L = s + 0.30s = 1.30s \]
- The breadth of the rectangle after a 20% increase is:
\[ B = s + 0.20s = 1.20s \]

### Step 4: Calculate the area of the rectangle.
The area \( A_{rectangle} \) of the rectangle is given by:
\[ A_{rectangle} = L \times B = (1.30s) \times (1.20s) \]
\[ A_{rectangle} = 1.30 \times 1.20 \times s^2 \]
\[ A_{rectangle} = 1.56s^2 \]

### Step 5: Calculate the increase in area.
The increase in area is:
\[ \text{Increase in area} = A_{rectangle} - A_{square} \]
\[ \text{Increase in area} = 1.56s^2 - s^2 = (1.56 - 1)s^2 = 0.56s^2 \]

### Step 6: Calculate the percentage increase in area.
To find the percentage increase in area, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in area}}{A_{square}} \right) \times 100 \]
\[ \text{Percentage Increase} = \left( \frac{0.56s^2}{s^2} \right) \times 100 = 56\% \]

### Conclusion:
The area of the rectangle exceeds the area of the square by **56%**.

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