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} (PR)/(PQ)=(PS)/(PT) \\ (12)/(12+8)=(21)/(PT) \\ PT=(20\cdot21)/(12) \\ PT=35 \end{gathered}`

So the length of PT is 35 units.