Đáp án:
Theo định lý Talet ta có:
a) EF // MN
$\begin{array}{l}
\Rightarrow \frac{{KE}}{{EM}} = \frac{{KF}}{{FN}}\\
\Rightarrow \frac{9}{{15}} = \frac{{12}}{{FN}}\\
\Rightarrow FN = 20\left( {cm} \right)\\
\Rightarrow KN = KF + FN = 12 + 20 = 32\left( {cm} \right)\\
b)Theo\,Talet:\frac{{KF}}{{KN}} = \frac{{EF}}{{MN}}\\
\Rightarrow \frac{{14}}{{MN}} = \frac{{12}}{{32}} = \frac{3}{8}\\
\Rightarrow MN = \frac{{112}}{3}\left( {cm} \right)
\end{array}$