If the triangles are similar, we can write the following proportion between the corresponding sides:
[tex]\begin{gathered} \frac{AB}{RS}=\frac{AC}{RT} \\ \\ \frac{6}{4}=\frac{9}{RT} \\ 6\cdot RT=9\cdot4 \\ 6RT=36 \\ RT=\frac{36}{6} \\ RT=6 \end{gathered}[/tex]
So the length of RT is 6 units.
