Since the sides RS and QT are parallel, these triangles are similar by case AA.
So we can write the following proportion between corresponding sides:
[tex]\begin{gathered} \frac{PR}{PQ}=\frac{PS}{PT} \\ \frac{12}{12+8}=\frac{21}{PT} \\ PT=\frac{20\cdot21}{12} \\ PT=35 \end{gathered}[/tex]
So the length of PT is 35 units.
