How do I find the base sides of this triangle?

Question

In the figure above, what is the Value of PT/PS ?

Answer 1

Well, since triangles $PQT$ and $PRS$ are similar (All three angles equal) I think that the proportion will also be the same between the sides.

$QT$ over $RS$ is 8/10, so the proportion of $PT$ over $PS$ should also be 8/10 (or 4/5) methinks.

Correct me if I'm wrong :)

Answer 2

Triangle $PRS$ similar to $PQT$.(Since all angles are equal.)

$$\frac{PR}{PQ}=\frac{PS}{PT}=\frac{RS}{QT}=\frac{10}{8}$$

$$\Rightarrow\frac{PT}{PS}= \frac{8}{10}=\frac{4}{5}$$ .

:)