CAYLEY 2020 Problem 22

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?

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Answer Choices
A. 3
B. \frac{11}{3}
C. \frac{15}{4}
D. \frac{7}{2}
E. 4