If the side of square is increased by 20% , then how much per cent does its area get increased :

Options

A. 0.4
B. 0.2
C. 0.44
D. 0.24

Answer

To solve the problem, we need to determine how much the area of a square increases when the side length is increased by 20%. Let's go through the steps systematically.

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

### Step 2: Calculate the original area
The area \( \text{Area}_{\text{original}} \) of the square is given by the formula:
\[ \text{Area}_{\text{original}} = A^2 \]

### Step 3: Calculate the new side length
If the side length is increased by 20%, the new side length \( A_{\text{new}} \) can be calculated as follows:
\[ A_{\text{new}} = A + 0.20A = 1.20A \]

### Step 4: Calculate the new area
Now, we calculate the area of the square with the new side length:
\[ \text{Area}_{\text{new}} = (A_{\text{new}})^2 = (1.20A)^2 = 1.44A^2 \]

### Step 5: Calculate the increase in area
The increase in area can be found by subtracting the original area from the new area:
\[ \text{Increase in Area} = \text{Area}_{\text{new}} - \text{Area}_{\text{original}} = 1.44A^2 - A^2 = 0.44A^2 \]

### Step 6: Calculate the percentage increase in area
To find the percentage increase in area, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Area}}{\text{Area}_{\text{original}}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left( \frac{0.44A^2}{A^2} \right) \times 100 = 44\% \]

### Final Answer
The area of the square increases by **44%** when the side length is increased by 20%.

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