a: \(CH=\dfrac{6^2}{4.5}=8\left(cm\right)\)
BC=BH+CH=12,5cm
\(AB=\sqrt{4.5\cdot12.5}=7.5\left(cm\right)\)
\(AC=\sqrt{8\cdot12.5}=10\left(cm\right)\)
b: \(AH=\sqrt{6^2-3^2}=3\sqrt{3}\left(cm\right)\)
\(BC=\dfrac{AB^2}{BH}=12\left(cm\right)\)
CH=BC-BH=9cm