If the area of a square is eighttimes, by what factor do itsw sides increase in length?
To find out the factor by which the sides of a square increase in length, we need to compare the square's area before and after the increase. Let's break down the steps to solve this problem:
1. Understand the problem: We are given that the area of the square after the increase is eight times the area before the increase. We need to determine the factor by which the sides increase in length.
2. Express the problem mathematically: Let's denote the original length of each side of the square as "x." The area of the square before the increase is x^2, and the area after the increase is 8x^2.
3. Set up the equation: Since we want to find the factor by which the sides increase, we can divide the area after the increase by the area before the increase:
(Area after increase) / (Area before increase) = (8x^2) / (x^2)
4. Solve the equation: Simplifying the equation:
8x^2 / x^2 = 8
The x^2 terms cancel out, leaving us with:
8 = 8
5. Interpret the result: The equation simplifies to 8 = 8, which ultimately means that the factor by which the sides increase in length is 1. In other words, the sides do not increase in length; they remain the same.
Therefore, the sides of the square do not increase in length.