\(\dfrac{BH}{HC}=\dfrac{9}{16}\Rightarrow BH=\dfrac{9}{16}HC\)
Áp dụng HTL tam giác
\(AH^2=BH\cdot HC\Rightarrow\dfrac{9}{16}HC^2=24^2=576\\ \Rightarrow HC^2=1024\Rightarrow HC=32\left(cm\right)\\ \Rightarrow HB=\dfrac{9}{16}\cdot32=18\left(cm\right)\\ \Rightarrow BC=BH+HC=50\)
Áp dụng HTL tam giác
\(\left\{{}\begin{matrix}AB^2=BH\cdot BC=18\cdot50=900\\AC^2=CH\cdot BC=32\cdot50=1600\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}AB=30\left(cm\right)\\AC=40\left(cm\right)\end{matrix}\right.\)
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