Medians BD and CE of triangle ABC are perpendicular, BD \equal{} 8, and CE \equal{} 12. The area of triangle ABC is
[asy]defaultpen(linewidth(.8pt));
dotfactor=4;pair A = origin;
pair B = (1.25,1);
pair C = (2,0);
pair D = midpoint(A--C);
pair E = midpoint(A--B);
pair G = intersectionpoint(E--C,B--D);dot(A);dot(B);dot(C);dot(D);dot(E);dot(G);
label("A",A,S);label("B",B,N);label("C",C,S);label("D",D,S);label("E",E,NW);label("G",G,NE);
draw(A--B--C--cycle);
draw(B--D);
draw(E--C);
draw(rightanglemark(C,G,D,3));[/asy]<spanclass=′latex−bold′>(A)</span>24<spanclass=′latex−bold′>(B)</span>32<spanclass=′latex−bold′>(C)</span>48<spanclass=′latex−bold′>(D)</span>64<spanclass=′latex−bold′>(E)</span>96