a: \(AH=\dfrac{AB\cdot AC}{BC}=4.8\left(cm\right)\)
b: \(\dfrac{BH}{HC}=\dfrac{7}{5}\)
nen HC=5/7BH
=>HC=5/12CB
\(HC=\dfrac{5}{12}\cdot10=\dfrac{50}{12}=\dfrac{25}{6}\left(cm\right)\)
\(HB=BC-HC=10-\dfrac{25}{6}=\dfrac{5}{6}\left(cm\right)\)
\(S_{ABH}=\dfrac{\dfrac{5}{6}\cdot4.8}{2}=2\left(cm^2\right)\)
\(S_{ACH}=\dfrac{\dfrac{25}{6}\cdot4.8}{2}=10\left(cm^2\right)\)