Triangles ABD and BCD are similar, because they are both right and share a common angle, and thus all three angles are equal.
This means that we can set the proportion
[tex]AB\div AD = BC\div DC[/tex]
Plug the numbers and we have
[tex]5\div 3.5 = 12\div x[/tex]
Solve for [tex]x[/tex]:
[tex]x=\dfrac{12\cdot 3.5}{5}=8.4[/tex]
