If the side of a square is increased by `30%`, its area is increased by

Options

A. `9%`
B. `30%`
C. `60%`
D. `69%`

Answer

To solve the problem of how much the area of a square increases when its side is increased by 30%, we can follow these steps:

### Step 1: Understand the relationship between side length and area of a square.
The area \( A \) of a square is given by the formula:
\[ A = \text{side}^2 \]

### Step 2: Let the original side length of the square be \( s \).
If the original side length is \( s \), then the original area \( A_1 \) is:
\[ A_1 = s^2 \]

### Step 3: Calculate the new side length after a 30% increase.
A 30% increase in the side length means the new side length \( s' \) is:
\[ s' = s + 0.3s = 1.3s \]

### Step 4: Calculate the new area with the increased side length.
The new area \( A_2 \) with the new side length \( s' \) is:
\[ A_2 = (s')^2 = (1.3s)^2 = 1.69s^2 \]

### Step 5: Determine the increase in area.
The increase in area \( \Delta A \) is given by:
\[ \Delta A = A_2 - A_1 = 1.69s^2 - s^2 = 0.69s^2 \]

### Step 6: Calculate the percentage increase in area.
To find the percentage increase in area, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\Delta A}{A_1} \right) \times 100 = \left( \frac{0.69s^2}{s^2} \right) \times 100 = 69\% \]

### Conclusion:
Thus, the area of the square increases by **69%** when the side is increased by 30%.

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