AHSME 1996 Problem 28

On a $4\times 4\times 3$ rectangular parallelepiped, vertices $A$, $B$, and $C$ are adjacent to vertex $D$. The perpendicular distance from $D$ to the plane containing $A$, $B$, and $C$ is closest to

$\text{(A)}\ 1.6 \text{(B)}\ 1.9 \text{(C)}\ 2.1 \text{(D)}\ 2.7 \text{(E)}\ 2.9$