Đáp án:
BC=BD+CD=17,5 (cm)
Theo t.c đường phân giác trong tam giác ta có:
$\begin{array}{l}
\dfrac{{AB}}{{BD}} = \dfrac{{AC}}{{CD}}\\
\Rightarrow \dfrac{{AB}}{{7,5}} = \dfrac{{AC}}{{10}}\\
\Rightarrow AB = \dfrac{3}{4}AC\\
\Rightarrow A{B^2} + A{C^2} = B{C^2}\\
\Rightarrow \dfrac{9}{{16}}A{C^2} + A{C^2} = 17,{5^2}\\
\Rightarrow AC = 14\left( {cm} \right)\\
\Rightarrow AB = \dfrac{{21}}{2}\left( {cm} \right)\\
\Rightarrow AH = \dfrac{{AB.AC}}{{BC}} = \dfrac{{14.\dfrac{{21}}{2}}}{{17,5}} = 8,4\left( {cm} \right)\\
\Rightarrow BH = \sqrt {A{B^2} - A{H^2}} = 6,3\left( {cm} \right)\\
\Rightarrow HD = BD - BH = 1,2\left( {cm} \right)
\end{array}$
