Given, AD=9, CE=12 and BE=16.
The length of side BC is,
[tex]BC=BE+CE=16+12=28[/tex]
In the given figure, DE and AC are parallel lines. Parallel lines divide triangle sides proportionally.
Hence,
[tex]\begin{gathered} \frac{BD}{AD}=\frac{BE}{CE} \\ \frac{BD}{9}=\frac{16}{12} \\ BD=\frac{16}{12}\times9 \\ =12 \end{gathered}[/tex]
Therefore, BD=12.
