If the area of a square is increased by 44%, retaining its sape as square, each of its sides increases by :

Options

A. `19%`
B. `21%`
C. `22%`
D. `20%`

Answer

To solve the problem of how much each side of a square increases when the area is increased by 44%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial Area**:
Let the initial area of the square be \( A \). For simplicity, we can assume \( A = 100 \) square units.

**Hint**: Start with a simple area to make calculations easier.

2. **Calculate the Increased Area**:
If the area is increased by 44%, the new area \( A' \) can be calculated as:
\[ A' = A + 0.44A = 1.44A \]
Substituting \( A = 100 \):
\[ A' = 1.44 \times 100 = 144 \text{ square units} \]

**Hint**: Remember that a percentage increase means adding that percentage of the original value to itself.

3. **Find the Side Lengths**:
The side length \( s \) of a square can be found using the formula \( s = \sqrt{A} \).
- For the original area:
\[ s = \sqrt{100} = 10 \text{ units} \]
- For the increased area:
\[ s' = \sqrt{144} = 12 \text{ units} \]

**Hint**: The side length of a square is the square root of its area.

4. **Calculate the Increase in Side Length**:
The increase in side length \( \Delta s \) is:
\[ \Delta s = s' - s = 12 - 10 = 2 \text{ units} \]

**Hint**: The increase is simply the difference between the new and old side lengths.

5. **Calculate the Percentage Increase**:
To find the percentage increase in side length, use the formula:
\[ \text{Percentage Increase} = \left( \frac{\Delta s}{s} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{2}{10} \right) \times 100 = 20\% \]

**Hint**: To find the percentage, divide the increase by the original value and multiply by 100.

### Final Answer:
Each side of the square increases by **20%**.