Given:
Given that the triangles ABD and CAD are similar.
The length of AB is 12.
The length of BD is x.
The length of AC is 27.
We need to determine the value of x.
Value of x:
Let us use the leg rule to determine the value of x.
Thus, we have;
[tex]\frac{BC}{AB}=\frac{AB}{BD}[/tex]
Substituting the values, we get;
[tex]\frac{27}{12}=\frac{12}{x}[/tex]
Cross multiplying, we get;
[tex]27x=12\times 12[/tex]
[tex]27x=144[/tex]
Dividing both sides by 27, we have;
[tex]x=\frac{16}{3}[/tex]
Thus, the value of x is [tex]\frac{16}{3}[/tex]
Hence, Option D is the correct answer.
