In the diagram, points $S$ and $T$ are on sides $Q R$ and $P Q$, respectively, of $\triangle P Q R$ so that $P S$ is perpendicular to $Q R$ and $R T$ is perpendicular to $P Q$. If $P T=1, T Q=4$, and $Q S=3$, what is the length of $S R$ ?
(A) 3
(B) $\frac{11}{3}$
(C) $\frac{15}{4}$
(D) $\frac{7}{2}$
(E) 4

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-022.jpg?height=341&width=455&top_left_y=2239&top_left_x=1255)