am/ab=(ac/2)/ab=(4/2)/(4+5+6)=2/15
bn/ab=(db/2)/ab=(6/2)/(4+5+6)=3/15
mn/ab=1-(am+bn)/ab=1-am/ab-bn/ab=1-2/15-3/15=10/15=2/3
所以：ab=mn/(2/3)=6*3/2=9
ab=9cm