Question

The triangle PQT with RS ll QT is shown below.If PR=12,RQ=8,and PS=21,what is the length of PT?

Answer 1

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:

$\begin{gathered} \frac{PR}{PQ}=\frac{PS}{PT} \\ \frac{12}{12+8}=\frac{21}{PT} \\ PT=\frac{20\cdot21}{12} \\ PT=35 \end{gathered}$

So the length of PT is 35 units.