The length of the side of a square (5.0 cm × 5.0 cm) is increased by 1%. By what percentage (%) the area of the square increases?
2 %
To determine the percentage increase in the area of a square when its side length is increased by 1%, we need to first understand the relationship between the side length of a square and its area.
Step-by-Step Solution:
- The original side length of the square is \(5.0 \, \text{cm}\).
- Calculate the original area of the square using the formula for the area of a square: \(A_{\text{original}} = \text{side}^2 = 5.0 \times 5.0 = 25.0 \, \text{cm}^2\).
- The side length is increased by 1%. The new side length becomes: \(\text{New side} = 5.0 + (1\% \, \text{of} \, 5.0) = 5.0 + 0.05 = 5.05 \, \text{cm}\).
- Calculate the new area of the square with the increased side length: \(A_{\text{new}} = \text{(New side)}^2 = 5.05 \times 5.05 = 25.5025 \, \text{cm}^2\).
- The increase in area can be calculated as: \(\Delta A = A_{\text{new}} - A_{\text{original}} = 25.5025 - 25.0 = 0.5025 \, \text{cm}^2\).
- The percentage increase in area is then calculated by: \(\text{Percentage Increase} = \left(\frac{\Delta A}{A_{\text{original}}}\right) \times 100 = \left(\frac{0.5025}{25.0}\right) \times 100 = 2.01\% \approx 2\%\).
Thus, the area of the square increases by approximately 2%.
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