8.1. If the width of a rectangle is increased by $30 \%$, and the height is decreased by $20 \%$, its perimeter will not change. Will the perimeter decrease or increase, and by what percentage, if instead the width of the original rectangle is decreased by $20 \%$, and the height is increased by $30 \%$?
Answer. It will increase by $10 \%$. Solution. Let the width of the original rectangle be $s$, and the height be $h$. In the first case, the modified width and height will be 1.3 and 0.8 $s$ respectively. According to the condition, $2(s+h)=2(1.3 s+0.8 h)$, from which $h=1.5 s$. This means that the original perimeter is $2(s+1.5 s)=5 s$. In the second case, the perimeter will be $2(0.8 s+1.3 h)=2(0.8 s+1.3 \cdot 1.5 s)=5.5$ s. This number is greater than $5 s$ by $0.5 s$, that is, by $10 \%$.