Look at the picture.
ΔABC and ΔDAC are similar. Therefore the sides of the triangles are in proportion:
[tex]\dfrac{AC}{BC}=\dfrac{DC}{AC}[/tex]
AC = x
BC = 5 + 4 = 9
DC = 4
Substitute:
[tex]\dfrac{x}{9}=\dfrac{4}{x}[/tex] cross multiply
[tex]x^2=(9)(4)\\\\x^2=36\to x=\sqrt{36}\\\\\boxed{x=6\to C)}[/tex]
