\(4AB=3BC\Leftrightarrow AB=\dfrac{3}{4}BC\)
Áp dụng HTL: \(AB^2=BH\cdot BC\Leftrightarrow\dfrac{9}{16}BC^2=\dfrac{12}{5}BC\Leftrightarrow BC\left(\dfrac{9}{16}BC-\dfrac{12}{5}\right)=0\\ \Leftrightarrow BC=\dfrac{12}{5}:\dfrac{9}{16}=\dfrac{64}{15}\left(cm\right)\\ \Leftrightarrow AB=\dfrac{16}{5}\left(cm\right)\)
Áp dụng HTL và PTG: \(\left\{{}\begin{matrix}AC=\sqrt{BC^2-AB^2}=\dfrac{16\sqrt{7}}{15}\left(cm\right)\\CH=\dfrac{AC^2}{BC}=\dfrac{28}{15}\left(cm\right)\end{matrix}\right.\)
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