Đáp án: $\dfrac{{25}}{{13}}\left( {cm} \right)$
Giải thích các bước giải:
$\begin{array}{l}
AB = 5cm;\dfrac{{AC}}{{AB}} = \dfrac{5}{{12}}\\
\Rightarrow AC = \dfrac{5}{{12}}.AB = \dfrac{{25}}{{12}}\left( {cm} \right)\\
\Rightarrow B{C^2} = A{B^2} + A{C^2} = {5^2} + {\left( {\dfrac{{25}}{{12}}} \right)^2} = \\
\Rightarrow BC = \dfrac{{65}}{{12}}\\
\Rightarrow {S_{ABC}} = \dfrac{1}{2}.AB.AC = \dfrac{1}{2}.AH.BC\\
\Rightarrow AH = \dfrac{{AB.AC}}{{BC}} = \dfrac{{25}}{{13}}\left( {cm} \right)
\end{array}$
