Question

question 8 of 10 what is the value of x in the figure below? in this diagram, △abd ~ △cad.

Explanation:

Step1: Use similarity of triangles property

Since $\triangle ABD\sim\triangle CAD$, we have the proportion $\frac{BD}{AD}=\frac{AD}{CD}$. Here $BD = x$, $AD = 12$, and $CD=27$. So, $\frac{x}{12}=\frac{12}{27}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{x}{12}=\frac{12}{27}$ gives us $27x=12\times12$.

Step3: Solve for x

$27x = 144$, then $x=\frac{144}{27}=\frac{16}{3}$.

Answer:

D. $\frac{16}{3}$