Đáp án:
$\begin{array}{l}
B1)\\
Do:MN \bot AB;CB \bot AB\\
\Rightarrow MN//CB\\
Theo\,Ta - let:\\
\dfrac{{MN}}{{BC}} = \dfrac{{AN}}{{AB}} = \dfrac{{1,5}}{6} = \dfrac{1}{4}\\
\Rightarrow \dfrac{{NB}}{{AB}} = 1 - \dfrac{1}{4} = \dfrac{3}{4}\\
\Rightarrow AB = NB:\dfrac{3}{4} = NB.\dfrac{4}{3} = 6.\dfrac{4}{3} = 8\left( {cm} \right)\\
B2)\\
Theo\,t/c:\dfrac{{BD}}{{AB}} = \dfrac{{DC}}{{AC}}\\
\Rightarrow \dfrac{{BD}}{4} = \dfrac{{DC}}{6} = \dfrac{{BD + DC}}{{4 + 6}} = \dfrac{{BC}}{{10}} = \dfrac{5}{{10}} = \dfrac{1}{2}\\
\Rightarrow \left\{ \begin{array}{l}
BD = \dfrac{1}{2}.4 = 2\left( {cm} \right)\\
DC = \dfrac{1}{2}.6 = 3\left( {cm} \right)
\end{array} \right.\\
Do:BE//AC\\
\Rightarrow \dfrac{{BE}}{{AC}} = \dfrac{{BD}}{{DC}}\left( {Theo\,Talet} \right)\\
\Rightarrow \dfrac{{BE}}{6} = \dfrac{2}{3}\\
\Rightarrow BE = \dfrac{2}{3}.6 = 4\left( {cm} \right)
\end{array}$
