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![](https://rs.olm.vn/images/avt/0.png?1311)
Áp dụng HTL tam giác:
\(\left\{{}\begin{matrix}AH^2=BH\cdot HC\\AB^2=BH\cdot BC\\AC^2=CH\cdot BC\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}HC=\dfrac{AH^2}{BH}=\dfrac{16}{3}\left(cm\right)\\AB^2=3\left(3+\dfrac{16}{3}\right)=25\left(cm\right)\\AC^2=\dfrac{16}{3}\left(3+\dfrac{16}{3}\right)=\dfrac{400}{9}\left(cm\right)\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}HC=\dfrac{16}{3}\left(cm\right)\\AB=5\left(cm\right)\\AC=\dfrac{20}{3}\left(cm\right)\end{matrix}\right.\)
\(BC=\sqrt{AB^2+AC^2}=\dfrac{25}{3}\left(cm\right)\left(pytago\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 2:
Xét ΔABC có
\(BC^2=AB^2+AC^2\)
nên ΔABC vuông tại A
Xét ΔABC vuông tại A có AH là đường cao ứng với cạnh huyền BC, ta được:
\(\left\{{}\begin{matrix}AB^2=BH\cdot BC\\AC^2=CH\cdot BC\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}BH=\dfrac{25}{13}\left(cm\right)\\CH=\dfrac{144}{13}\left(cm\right)\end{matrix}\right.\)
Bài 1:
Ta có: \(\dfrac{AB}{AC}=\dfrac{5}{6}\)
\(\Leftrightarrow HB=\dfrac{25}{36}HC\)
Ta có: \(AH^2=HB\cdot HC\)
\(\Leftrightarrow HC^2\cdot\dfrac{25}{36}=900\)
\(\Leftrightarrow HC=36\left(cm\right)\)
hay HB=25(cm)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1,\dfrac{AB}{AC}=\dfrac{5}{6}\Leftrightarrow AB=\dfrac{5}{6}AC\)
Áp dụng HTL tam giác
\(\dfrac{1}{AH^2}=\dfrac{1}{AB^2}+\dfrac{1}{AC^2}\Leftrightarrow\dfrac{1}{900}=\dfrac{1}{\dfrac{25}{36}AC^2}+\dfrac{1}{AC^2}\\ \Leftrightarrow\dfrac{1}{900}=\dfrac{36}{25AC^2}+\dfrac{1}{AC^2}\\ \Leftrightarrow\dfrac{1}{900}=\dfrac{36+25}{25AC^2}\Leftrightarrow\dfrac{1}{900}=\dfrac{61}{25AC^2}\\ \Leftrightarrow25AC^2=54900\Leftrightarrow AC^2=2196\Leftrightarrow AC=6\sqrt{61}\left(cm\right)\\ \Leftrightarrow AB=\dfrac{5}{6}\cdot6\sqrt{61}=5\sqrt{61}\\ \Leftrightarrow BC=\sqrt{AB^2+AC^2}=61\left(cm\right)\)
Áp dụng HTL tam giác:
\(\left\{{}\begin{matrix}AB^2=BH\cdot BC\\AC^2=CH\cdot BC\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}BH=\dfrac{AB^2}{BC}=...\\CH=\dfrac{AC^2}{BC}=...\end{matrix}\right.\)
Bài 1:
Ta có: \(\dfrac{AB}{AC}=\dfrac{5}{6}\)
\(\Leftrightarrow HB=\dfrac{25}{36}HC\)
Ta có: \(AH^2=HB\cdot HC\)
\(\Leftrightarrow HC^2\cdot\dfrac{25}{36}=900\)
\(\Leftrightarrow HC=36\left(cm\right)\)
hay HB=25(cm)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 2:
Ta có: \(\dfrac{HB}{HC}=\dfrac{1}{3}\)
nên HC=3HB
Ta có: \(AH^2=HB\cdot HC\)
\(\Leftrightarrow HB^2=48\)
\(\Leftrightarrow HB=4\sqrt{3}\left(cm\right)\)
\(\Leftrightarrow BC=4\cdot HB=16\sqrt{3}\left(cm\right)\)
Bài 1:
ta có: \(AB=\dfrac{1}{2}AC\)
\(\Leftrightarrow\dfrac{HB}{HC}=\dfrac{1}{4}\)
\(\Leftrightarrow HC=4HB\)
Ta có: \(AH^2=HB\cdot HC\)
\(\Leftrightarrow HB=1\left(cm\right)\)
\(\Leftrightarrow HC=4\left(cm\right)\)
hay BC=5(cm)
Xét ΔBAC vuông tại A có AH là đường cao ứng với cạnh huyền BC
nên \(\left\{{}\begin{matrix}AB^2=HB\cdot BC\\AC^2=HC\cdot BC\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}AB=\sqrt{5}\left(cm\right)\\AC=2\sqrt{5}\left(cm\right)\end{matrix}\right.\)
Lời giải:
Áp dụng định lý Pitago cho tam giác vuông $ABH$:
$BH=\sqrt{AB^2-AH^2}=\sqrt{5^2-4^2}=3$ (cm)
Áp dụng hệ thức lượng trong tam giác vuông:
$AH^2=BH.CH\Rightarrow CH=\frac{AH^2}{BH}=\frac{4^2}{3}=\frac{16}{3}$ (cm)
$BC=BH+CH=3+\frac{16}{3}=\frac{25}{3}$ (cm)
$AC=\sqrt{AH^2+CH^2}=\sqrt{4^2+(\frac{16}{3})^2}=\frac{20}{3}$ (cm)
Hình vẽ:
![](data:image/png;base64,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)