In △ABC, AB=13, BC=14 and CA=15. Also, M is the midpoint of side AB and H is the foot of the altitude from A to BC. The length of HM is[asy]
size(200);
defaultpen(linewidth(0.7)+fontsize(10));
pair H=origin, A=(0,6), B=(-4,0), C=(5,0), M=B+3.6*dir(B--A);
draw(B--C--A--B^^M--H--A^^rightanglemark(A,H,C));
label("A", A, NE);
label("B", B, W);
label("C", C, E);
label("H", H, S);
label("M", M, dir(M));
[/asy]<spanclass=′latex−bold′>(A)</span>6<spanclass=′latex−bold′>(B)</span>6.5<spanclass=′latex−bold′>(C)</span>7<spanclass=′latex−bold′>(D)</span>7.5<spanclass=′latex−bold′>(E)</span>8