If a side of a square increases by 0.5%, find the approximate percentage increase in the area
To find the approximate percentage increase in the area when the side of a square increases by 0.5%, we can use the formula for the area of a square, which is A = s^2, where A is the area and s is the side length.
Let's say the original side length of the square is s.
When the side length increases by 0.5%, the new side length becomes s + 0.5% of s.
This can be written as s + 0.005s, which simplifies to 1.005s.
The new area of the square is (1.005s)^2 = 1.010025s^2.
The increase in the area is the difference between the new area and the original area: 1.010025s^2 - s^2 = 0.010025s^2.
To find the percentage increase, we divide the increase in area by the original area and then multiply by 100:
(0.010025s^2 / s^2) * 100 = 1.0025 * 100 = 1.0025%.
Therefore, the approximate percentage increase in the area is 1.0025%.
To find the approximate percentage increase in the area of a square when one of its sides increases by 0.5%, we can follow these steps:
Step 1: Let's assume the initial side length of the square is represented by "x".
Step 2: The area of the square is given by the formula A = x^2.
Step 3: If the side length increases by 0.5%, the new side length would be x + 0.005x = 1.005x.
Step 4: The new area of the square, A', can be calculated by substituting the new side length into the area formula: A' = (1.005x)^2 = 1.010025x^2.
Step 5: The percentage increase in the area can be determined by subtracting the initial area from the new area, dividing the result by the initial area, and multiplying by 100.
Expressed as a formula, it would be: Percentage increase in area = (A' - A) / A * 100 = (1.010025x^2 - x^2) / x^2 * 100 = (1.010025 - 1) * 100 = 0.010025 * 100 ≈ 1.0025%.
Therefore, there is an approximate 1.0025% increase in the area of the square when one of its sides increases by 0.5%.