On increasing the length of each side of a square by 20%, the percentage increase in its area is :

Question

Accepted Answer

To determine the percentage increase in the area of a square when each side is increased by 20%, we can follow these steps:

1. **Initial Area Calculation:**
   - Let the original side length of the square be $ s $.
   - The original area of the square is $ s^2 $.

2. **New Side Length Calculation:**
   - When the side length is increased by 20%, the new side length becomes $ s + 0.2s = 1.2s $.

3. **New Area Calculation:**
   - The new area of the square with the increased side length is $ (1.2s)^2 = 1.44s^2 $.

4. **Percentage Increase in Area:**
   - The increase in area is $ 1.44s^2 - s^2 = 0.44s^2 $.
   - To find the percentage increase, we use the formula:
     $$
     \text{Percentage Increase} = \left(\frac{\text{Increase in Area}}{\text{Original Area}}\right) \times 100 = \left(\frac{0.44s^2}{s^2}\right) \times 100 = 44\%
     $$

Therefore, the percentage increase in the area is 44%, which corresponds to Option 1 (0.44 when expressed as a decimal fraction of 1).

**Explanation for Incorrect Options:**

- **Option 2 (0.4):** This option suggests a 40% increase in area. However, as calculated, the actual increase is 44%, not 40%. Therefore, this option is incorrect.

- **Option 3 (0.2):** This option implies a 20% increase in area. This is incorrect because the increase in area is significantly higher due to the quadratic nature of area calculation (since area is proportional to the square of the side length).

- **Option 4 (0.22):** This option suggests a 22% increase in area. Again, this is incorrect because the actual increase is 44%, as derived from the calculations above.

In conclusion, the correct answer is Option 1, which accurately reflects the 44% increase in the area of the square when each side is increased by 20%.