In the diagram, what is the perimeter of $\triangle P Q R$ ?
(A) 63
(B) 60
(C) 55
(D) 85
(E) 70

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-093.jpg?height=274&width=377&top_left_y=1820&top_left_x=1248)
Each of $\triangle P S Q$ and $\triangle R S Q$ is right-angled at $S$, so we can use the Pythagorean Theorem in both triangles.

In $\triangle R S Q$, we have $Q S^{2}=Q R^{2}-S R^{2}=25^{2}-20^{2}=625-400=225$, so $Q S=\sqrt{225}=15$ since $Q S>0$.

In $\triangle P S Q$, we have $P Q^{2}=P S^{2}+Q S^{2}=8^{2}+225=64+225=289$, so $P Q=\sqrt{289}=17$ since $P Q>0$.

Therefore, the perimeter of $\triangle P Q R$ is $P Q+Q R+R P=17+25+(20+8)=70$.

ANsWER: (E)