Đáp án:
a) MN//BC theo Ta let ta có:
$\begin{array}{l}
\frac{{AM}}{{AB}} = \frac{{AN}}{{AC}}\\
\Rightarrow \frac{4}{{4 + x}} = \frac{5}{{8,5}}\\
\Rightarrow 4.8,5 = 5\left( {4 + x} \right)\\
\Rightarrow 34 = 20 + 5x\\
\Rightarrow x = 2,8\left( {cm} \right)\\
b)PQ//EF\\
\Rightarrow \frac{{DP}}{{DE}} = \frac{{DQ}}{{DF}}\\
\Rightarrow \frac{x}{{x + 10,5}} = \frac{9}{{24}}\\
\Rightarrow 24x = 9\left( {x + 10,5} \right)\\
\Rightarrow 24x = 9x + 94,5\\
\Rightarrow 15x = 94,5\\
\Rightarrow x = 6,3\left( {cm} \right)
\end{array}$
