2017 Pascal Problem 22

In the diagram, UVWX is a rectangle that lies flat on a horizontal floor. A vertical semi-circular wall with diameter XW is constructed. Point Z is the highest point on this wall. If UV = 20 and VW = 30, the perimeter of \triangle UVZ is closest to

\textbf{(A)}\ 95\quad \textbf{(B)}\ 86\quad \textbf{(C)}\ 102\quad \textbf{(D)}\ 83\quad \textbf{(E)}\ 92

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.