Let's begin by listing out the information given to us:
|CD| = 9.5, |CE| = 13.75, |AC| = 13.75 + 5.5 = 19.25, |BC| = 9.5 + x
Using Triangle proportionality theorem, we have:
[tex]\begin{gathered} |CE|\colon|EA|=|CD|\colon|DB| \\ 13.75\colon5.5=9.5\colon x\Rightarrow\frac{13.75}{5.5}=\frac{9.5}{x} \\ 13.75x=5.5\cdot9.5 \\ \frac{13.75x}{13.75}=\frac{5.5\cdot9.5}{13.75}\Rightarrow x=\frac{5.5\cdot9.5}{13.75} \\ x=3.8 \\ \\ \therefore|BD|=3.8 \end{gathered}[/tex]
