8.2. One side of the rectangle (width) was increased by $10 \%$, and the other (length) - by $20 \%$. a) Could the perimeter increase by more than 20\%? b) Find the ratio of the sides of the original rectangle if it is known that the perimeter of the new rectangle is $18 \%$ larger than the perimeter of the original?
Answer. a) could not; b) 1:4. Solution. a) Let $a$ and $b$ be the sides of the original rectangle. Then the sides of the new rectangle are $1.1a$ and $1.2b$, and its perimeter is $2(1.1a + 1.2b) < 2(1.12(a + b))$. Therefore, the perimeter increased by less than $20\%$. b) See problem 7.2 b).