Answer:
Option C.
Step-by-step explanation:
Given information: [tex]\triangle ABD\sim \triangle CAD[/tex], AB=12, BD=x, BC=27.
In triangle ABC and triangle DBA,
[tex]\angle BAC=\angle BDA=90^{\circ}[/tex]
[tex]\angle ABC=\angle DBA[/tex] (Reflexive property)
By AA property of similarity triangle ABC and triangle DBA are similar.
The corresponding parts of similar triangles are proportional.
[tex]\dfrac{AB}{CB}=\dfrac{BD}{BA}[/tex]
[tex]\dfrac{12}{27}=\dfrac{x}{12}[/tex]
Multiply both sides by 12.
[tex]\dfrac{12}{27}\times 12=\dfrac{x}{12}\times 12[/tex]
[tex]\dfrac{144}{27}=x[/tex]
[tex]\dfrac{16}{3}=x[/tex]
Therefore, the correct option is C.
