Triangle ABE is similar to traingle ACD; in similar triangles, corresponding sides are always in the same ratio:
[tex]\frac{DC}{EB}=\frac{AC}{AB}[/tex]
Use the equation above to find the length of x:
[tex]\begin{gathered} \frac{x}{4}=\frac{6+9}{6} \\ \\ \frac{x}{4}=\frac{15}{6} \\ \\ x=4\cdot\frac{15}{6} \\ \\ x=\frac{60}{6} \\ \\ x=10 \end{gathered}[/tex]Then, the length of x is 10
