Giả sử: \(BH< CH\) \(\left(BH;CH>0\right)\)
Áp dụng hệ thức lượng, ta có:
\(AH^2=BH.CH=2,4^2=5,76\left(cm\right)\)
\(\Rightarrow x=\dfrac{5,76}{CH}\left(cm\right)\)
Ta có: \(BC=BH+CH=5\left(cm\right)\)
\(\Rightarrow x+CH=5\)
\(\Leftrightarrow\dfrac{5,76}{CH}+CH=5\)
\(\Leftrightarrow5,76+CH^2=5CH\)
\(\Leftrightarrow\left[{}\begin{matrix}CH=3,2\left(tm\right)\\CH=1,8\left(tm\right)\end{matrix}\right.\) \(\rightarrow\left[{}\begin{matrix}BH=1,8\left(tm\right)\\BH=3,2\left(ktm\right)\end{matrix}\right.\)
Áp dụng hệ thức lượng, ta có:
`@`\(AB^2=BH.BH\)
\(\Rightarrow AB=\sqrt{1,8.5}=\sqrt{9}=3\left(cm\right)\)
`@`\(AC^2=CH.BC\)
\(\Rightarrow AC=\sqrt{3,2.5}=\sqrt{16}=4\left(cm\right)\)
