\(BC=BH+CH=7\left(cm\right)\)
Áp dụng HTL tam giác:
\(\left\{{}\begin{matrix}AH^2=BH\cdot HC=12\\AB^2=BH\cdot BC=28\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}AH=2\sqrt{3}\left(cm\right)\\AB=2\sqrt{7}\left(cm\right)\end{matrix}\right.\)
Ta có \(AC=\sqrt{BC^2-AB^2}=\sqrt{21}\left(cm\right)\)
\(S_{ABC}=\dfrac{1}{2}AH\cdot BC=\dfrac{1}{2}\cdot2\sqrt{3}\cdot7=7\sqrt{3}\left(cm^2\right)\)
\(P_{ABC}=AB+BC+AC=\sqrt{21}+2\sqrt{7}+7\left(cm\right)\)
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