The length and breadth of square are increased by 40% and 30% respectively. The area of resulting rectangle exceeds the area of the square by:

Options

A. 42%
B. 62%
C. 82%
D. 52%

Answer

To solve the problem step by step, we will first define the dimensions of the square, then calculate the new dimensions after the increases, and finally find the difference in areas.

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

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

### Step 3: Calculate the new dimensions of the rectangle
The length of the rectangle after a 40% increase will be:
\[ \text{Length} = s + 0.4s = 1.4s \]
The breadth of the rectangle after a 30% increase will be:
\[ \text{Breadth} = s + 0.3s = 1.3s \]

### Step 4: Calculate the area of the rectangle
The area of the rectangle \( A_r \) is given by:
\[ A_r = \text{Length} \times \text{Breadth} = (1.4s) \times (1.3s) = 1.82s^2 \]

### Step 5: Find the difference in areas
Now, we need to find how much the area of the rectangle exceeds the area of the square:
\[ \text{Difference} = A_r - A_s = 1.82s^2 - s^2 = 0.82s^2 \]

### Step 6: Calculate the percentage increase in area
To find the percentage by which the area of the rectangle exceeds the area of the square, we can use the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Difference}}{A_s} \right) \times 100 = \left( \frac{0.82s^2}{s^2} \right) \times 100 = 82\% \]

### Final Answer
The area of the resulting rectangle exceeds the area of the square by **82%**.

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