Answer:
[tex]x = \frac{22}{3}[/tex]
Step-by-step explanation:
Since both CB and ED intersect AD perpendicularly, we can say they are parallel and that ΔACB is similar to ΔAED from Thales intercept theorem. Now, we can set up a proportion from the definition of similar triangles:
[tex]\frac{AB}{AD} = \frac{BC}{DE}[/tex]
We can say that AD = AB + BD(segment addition postulate) and substitute to get AD = 11. Now we can plug in the numbers we have to the proportion:
[tex]\frac{6}{11} =\frac{4}{x}[/tex]
We can cross-multiply to get:
[tex]6x = 44[/tex]
and divide by 6 to get
[tex]x = \frac{22}{3}[/tex]
