Problem 5. The length of segment $A B$ is 2 cm longer than the length of segment $C D$. If the length of segment $C D$ is tripled, and the length of segment $A B$ is increased by $10 \mathrm{~cm}$, equal segments will be obtained. What are the lengths of segments $A B$ and $C D$?
Solution. From the drawing, it is clear that when the segment $CD$ is tripled, we have increased it by 2 of its lengths, and this increase is $2+10=12 \mathrm{~cm}$.

![](https://cdn.mathpix.com/cropped/2024_06_05_d4fd26fa5c16caf575adg-2.jpg?height=190&width=503&top_left_y=359&top_left_x=979)
Therefore,

$$
\overline{CD}=12: 2=6 \mathrm{~cm} \text { and } \overline{AB}=6+2=8 \mathrm{~cm}
$$

## V section