If sides of a square are increased by `7%` , by what percent its area will be increased?

Options

A. `14%`
B. `49%`
C. `14.49%`
D. `7%`

Answer

To solve the problem of how much the area of a square increases when its sides are increased by 7%, we can follow these steps:

### Step 1: Understand the original area of the square.
Let the original side length of the square be \( s \). The area \( A \) of the square is given by the formula:
\[ A = s^2 \]

### Step 2: Calculate the new side length after the increase.
If the side length is increased by 7%, the new side length \( s' \) can be calculated as:
\[ s' = s + 0.07s = 1.07s \]

### Step 3: Calculate the new area of the square.
The new area \( A' \) of the square with the new side length \( s' \) is:
\[ A' = (s')^2 = (1.07s)^2 \]
Expanding this, we get:
\[ A' = 1.1449s^2 \]

### Step 4: Calculate the increase in area.
The increase in area \( \Delta A \) is given by:
\[ \Delta A = A' - A = 1.1449s^2 - s^2 = (1.1449 - 1)s^2 = 0.1449s^2 \]

### Step 5: Calculate the percentage increase in area.
To find the percentage increase in area, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\Delta A}{A} \right) \times 100 \]
Substituting the values we calculated:
\[ \text{Percentage Increase} = \left( \frac{0.1449s^2}{s^2} \right) \times 100 = 0.1449 \times 100 = 14.49\% \]

### Conclusion:
The area of the square will increase by approximately **14.49%** when the sides are increased by 7%.

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