[tex]\rule{0.2}{0.2}_{ AD-median\breve a\ \Rightarrow BD=CD=BC:2=10:2=5\ cm} \\ \\ \rule{0.2}{0.2}_{\mathcal{P}_{ABD}=AB+AD+BD=18 \Rightarrow AB+AD+5=18\bigg|_{-5} \Rightarrow AB+AD=13\ cm\ \ \ (1)}\\ \\ \rule{0.2}{0.2}_{\mathcal{P}_{ACD}=AC+AD+CD=16 \Rightarrow AC+AD+5=16\bigg|_{-5} \Rightarrow AC+AD=11\ cm\ \ \ (2)}\\ \\ \rule{0.2}{0.2}_{\mathcal{P}_{ABC}=AB+AC+BC=24 \Rightarrow AB+AC+10=24\bigg|_{-10} \Rightarrow AB+AC=14\ cm\ \ \ (3)}\\ \\[/tex]
[tex]\it \rule{0.2}{0.2}_{(1),\ (2) \Rightarrow\ AB+AD-AC-AD=13-11 \Rightarrow AB-AC=2\ \ \ \ \ \ (4)}\\ \\ \rule{0.2}{0.2}_{(3),\ (4) \Rightarrow\ 2AB=16 \Rightarrow AB=8\ cm[/tex]
