Answer
The length of the side DB is \[6\].
Work Step by Step
\[\Delta ABC\] and \[\Delta ADE\]are similar where, BA\[=\]3, CB\[=\]3 in \[\Delta ABC\] and ED\[=\]9, EA\[=\]15 in \[\Delta ADE\].
Let DB\[=x\]. DA can be computed by adding up the DB and BA.
\[\begin{align}
& DA=DB+BA \\
& DA=x+3
\end{align}\]
Thus, \[\frac{ED}{CB}=\frac{DA}{BA}\]
Compute DB by applying the cross multiplication principle for proportion that states that if\[\frac{a}{b}=\frac{c}{d}\], then \[ad=bc\].
\[\begin{align}
& \frac{9}{3}=\frac{x+3}{3} \\
& 3\times (x+3)=9\times 3 \\
& 3x+9=27 \\
& 3x=27-9
\end{align}\]
\[\begin{align}
& 3x=18 \\
& x=6
\end{align}\]
