1997 AMC 12 第 15 题

View $BD$ and $CE$ as the diagonals of quadrilateral $BCDE$

Triangle $ADE$ is similar to $ABC$ with scale factor $\frac{1}{2}$

Quadrilateral $BCDE$ has perpendicular diagonals $BD=8$ and $CE=12,$ so its area is $\frac12(8)(12)=48.$ Since $D,E$ are midpoints, triangle $ADE$ has one fourth the area of $ABC,$ making $BCDE$ three fourths of it. Thus $[ABC]=\frac{48\cdot4}{3}=64,$ so D is correct.