The area of a rectangle has increased by 5%. The length of one side was decreased by 10%. By what percentage was the other side increased? Give your answer correct to the nearest integer.

Answer 1

Let the original length of one side of the rectangle be $x$. Since the area has increased by 5%, the new area of the rectangle is $1.05$ times the original area, or $x(x) = 1.05x^2$. Dividing both sides by $1.05$, we find $x^2 = \frac{1}{1.05}$, so $x = \sqrt{\frac{1}{1.05}}$. Therefore, the new length of that side is $0.9767x$, which is a decrease of $100\%-97.67\% = 2.33\%$. Since the length of the other side has increased proportionally, the answer is $\boxed{2}$.