AMC 10 2020a Problem 12

Triangle $AMC$ is isosceles with $AM = AC$. Medians $\overline{MV}$ and $\overline{CU}$ are perpendicular to each other, and $MV=CU=12$. What is the area of $\triangle AMC?$

$\textbf{(A) } 48 \textbf{(B) } 72 \textbf{(C) } 96 \textbf{(D) } 144 \textbf{(E) } 192$