6. One side of a rectangle is $5 \mathrm{~cm}$, and the other is the smallest two-digit number that is divisible by 3. For the second rectangle, one side is equal to the shorter side of the first. The area of one rectangle is $25 \mathrm{~cm}^{2}$ greater than the area of the other. Determine the unknown side of the second rectangle.
6. First, let's determine the unknown side of the rectangle. For this, we will find the smallest two-digit number that is divisible by 3, which is 12. According to the problem, one side of the second rectangle is $5 \mathrm{~cm}$. Let's determine the area of the first rectangle $(12 \times 5=60)$. Since the problem does not specify which rectangle's area is larger by $25 \mathrm{~cm}^{2}$, we need to consider two cases.

First case. Suppose the area of the first rectangle is $25 \mathrm{~cm}^{2}$ larger than the area of the second rectangle. In this case, the area of the second rectangle is $35 \mathrm{~cm}^{2}(60-25=35)$. Knowing that one side of the second rectangle is 5 cm and its area is 35 $\mathrm{cm}^{2}$, we can determine the second side $-7 \mathrm{~cm}(35: 5=7)$.

Second case. Suppose the area of the second rectangle is $25 \mathrm{~cm}^{2}$ larger than the area of the first rectangle. In this case, the area of the second rectangle is $85 \mathrm{~cm}^{2}(60+25=85)$. Knowing that one side of the second rectangle is 5 cm and its area is 85 $\mathrm{cm}^{2}$, we can determine the second side $-17 \mathrm{~cm}(85: 5=17)$.

Answer: 7 cm or 17 cm.