1. A rectangle is drawn on the board. It is known that if its width is increased by $30 \%$, and its length is decreased by $20 \%$, then its perimeter remains unchanged. How would the perimeter of the original rectangle change if its width were decreased by $20 \%$, and its length were increased by $30 \%$?
Answer. It will increase by $10 \%$.

Solution. Let's denote the width of the original rectangle as $a$, and the height as $b$. In the first case, the modified width and length will be $1.3a$ and $0.8b$ respectively. According to the condition, $2(a+b) = 2(1.3a + 0.8b)$, from which we get $b = 1.5a$. This means the original perimeter is $2(a + 1.5a) = 5a$. In the second case, the perimeter will be $2(0.8a + 1.3b) = 2(0.8a + 1.3 \cdot 1.5a) = 5.5a$. This number is greater than $5a$ by $0.5a$, which is $10 \%$.