Bài 3:
Ta có: \(\left\{{}\begin{matrix}BD\perp AC.\\AE\perp AC.\end{matrix}\right.\)
\(\Rightarrow BD//AE\) (Từ vuông góc đến song song).
Xét \(\Delta ACE:\)
\(BD//AE\left(cmt\right).\)
\(\Rightarrow\dfrac{BD}{AE}=\dfrac{BC}{AC}\) (Talet đảo).
Thay: \(\dfrac{2,5}{AE}=\dfrac{2}{5}.\)
\(\Rightarrow AE=6,25cm.\)