Answer
$\bf{I}$
Work Step by Step
We are given that the two right triangles are similar. This implies that their sides must be proportional.
That is, $\dfrac{\overline{PT}}{\overline{TS}}=\dfrac{\overline{PQ}}{\overline{RS}}$
or, $\dfrac{15}{\overline{TS}}=\dfrac{18}{6}$
or, $\overline{TS}=5$
Now, $\overline{PS}=\overline{PT}+\overline{TS}=15+5=20$
Therefore, the correct option is $\bf{I}$.
