\(BH=\sqrt{5^2-4^2}=3\left(cm\right)\)
\(AC=\sqrt{4^2+12^2}=4\sqrt{10}\left(cm\right)\)
BC=3+12=15(cm)
\(C=AB+BC+AC=15+5+4\sqrt{10}=20+4\sqrt{10}\left(cm\right)\)
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