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

The triangle PQT with RS ll QT is shown below.If PR=12,RQ=8,and PS=21,what is the-example-1
The triangle PQT with RS ll QT is shown below.If PR=12,RQ=8,and PS=21,what is the-example-1
The triangle PQT with RS ll QT is shown below.If PR=12,RQ=8,and PS=21,what is the-example-2

1 Answer

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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.

User Amani
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