4. Given is a parallelogram $A B C D$ with side lengths $12 \mathrm{~cm}$ and $8 \mathrm{~cm}$. The longer side $\overline{A B}$ is extended beyond point $B$ by $5 \mathrm{~cm}$ to obtain point $E$. The lines $E C$ and $A D$ intersect at point $F$. Calculate $|D F|$.
4. 

![](https://cdn.mathpix.com/cropped/2024_05_30_5f1c108ea9147169b9fdg-1.jpg?height=451&width=411&top_left_y=1902&top_left_x=366)

According to Tales' theorem on proportional segments, the ratio is: $|D F|:|A F|=|D C|:|A E|$.

1 POINT

$x:(x+8)=12: 17$ which means $17x=12x+96$ so $x=19.2$.

Therefore, $|D F|=19.2 \text{ cm}$.