Question

Cho ΔABC vuông tại A, AH⊥BC, AH= 2,4 cm và BC = 5cm.Tính AB,AC,BH ?

CÁC BẠN GIÚP MÌNH VS MINH CẢM ƠN !

Answer 1

\(\left\{{}\begin{matrix}AB.AC=AH.BC\\AB^2+AC^2=BC^2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}AB.AC=12\\AB^2+AC^2=25\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}AC=\frac{12}{AB}\\AB^2+AC^2=25\end{matrix}\right.\)

\(\Rightarrow AB^2+\frac{144}{AB^2}=25\)

\(\Leftrightarrow AB^4-25AB^2+144=0\Rightarrow\left[{}\begin{matrix}AB^2=16\\AB^2=9\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}AB=4\Rightarrow AC=3\Rightarrow BH=\frac{AB^2}{BC}=\frac{16}{5}\\AB=3\Rightarrow AC=4\Rightarrow BH=\frac{AB^2}{BC}=\frac{9}{5}\end{matrix}\right.\)