a: \(HC=\dfrac{6^2}{4.5}=8\left(cm\right)\)
BC=BH+CH=12,5(cm)
\(AB=\sqrt{4.5\cdot12.5}=7.5\left(cm\right)\)
\(AC=\sqrt{8\cdot12.5}=10\left(cm\right)\)
b: \(AH=\sqrt{6^2-3^2}=3\sqrt{3}\left(cm\right)\)
\(CH=\dfrac{27}{3}=9\left(cm\right)\)
\(AC=\sqrt{9\cdot12}=6\sqrt{3}\left(cm\right)\)