In the diagram, $P Q=19, Q R=18$, and $P R=17$. Point $S$ is on $P Q$, point $T$ is on $P R$, and point $U$ is on $S T$ so that $Q S=S U$ and $U T=T R$. The perimeter of $\triangle P S T$ is equal to
(A) 36
(B) 35
(C) 37
(D) 34
(E) 38

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-064.jpg?height=415&width=444&top_left_y=882&top_left_x=1274)
We have

$$
\text { Perimeter of } \triangle P S T \text { } \begin{aligned}
& \triangle S+S T+P T \\
&=P S+(S U+U T)+P T \\
&=P S+S Q+T R+P T \quad(\text { since } S U=S Q \text { and } U T=T R) \\
&=(P S+S Q)+(P T+T R) \\
&=P Q+P R \\
&=19+17 \\
&=36
\end{aligned}
$$

Therefore, the perimeter of $\triangle P Q R$ is 36 .

ANSWER: (A)