Question

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Answer 1

\(\dfrac{AB}{AC}=\dfrac{5}{6}\Rightarrow AB=\dfrac{5}{6}AC\)

Áp dụng PTG: \(AB^2+AC^2=\dfrac{25}{36}AC^2+AC^2=BC^2\)

\(\Rightarrow BC^2=\dfrac{61}{36}AC^2\\ \Rightarrow BC=\dfrac{\sqrt{61}}{6}AC\)

Áp dụng HTL: \(\dfrac{AB\cdot AC}{BC}=AH=30\)

\(\Rightarrow\dfrac{\dfrac{5}{6}AC^2}{\dfrac{\sqrt{61}}{6}AC}=30\\ \Rightarrow\dfrac{5}{\sqrt{61}}AC=30\\ \Rightarrow AC=6\sqrt{61}\left(dm\right)\\ \Rightarrow AB=\dfrac{5}{6}\cdot6\sqrt{61}=5\sqrt{61}\left(dm\right)\\ BC=\dfrac{\sqrt{61}}{6}\cdot6\sqrt{61}=61\left(dm\right)\)

Áp dụng HTL: \(BH=\dfrac{AB^2}{BC}=25\left(dm\right)\)