In the diagram, what is the perimeter of $\triangle P Q S$ ?
(A) 74
(B) 55
(C) 80
(D) 84
(E) 97

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-100.jpg?height=401&width=352&top_left_y=217&top_left_x=1296)
By the Pythagorean Theorem in $\triangle P Q R, P Q^{2}=P R^{2}-Q R^{2}=13^{2}-5^{2}=144$, so $P Q=\sqrt{144}=12$.

By the Pythagorean Theorem in $\triangle P Q S, Q S^{2}=P S^{2}-P Q^{2}=37^{2}-12^{2}=1225$, so $Q S=\sqrt{1225}=35$.

Therefore, the perimeter of $\triangle P Q S$ is $12+35+37=84$.

ANSWER: (D)