Question

question 5 of 10 what is the value of x in the figure below? in this diagram, △abd ~ △cad. c 10 d 3 b a. $\frac{10}{13}$ b. $sqrt{130}$ c. 13 d. $sqrt{65}$ e. $sqrt{30}$ f. 30

Explanation:

Step1: Use similarity of triangles

Since $\triangle ABD\sim\triangle CAD$, we have $\frac{BD}{AD}=\frac{AD}{CD}$, so $AD^{2}=BD\times CD$.

Step2: Substitute values

Given $BD = 3$ and $CD = 10$, then $x^{2}=3\times10$.

Step3: Solve for x

$x=\sqrt{30}$.

Answer:

E. $\sqrt{30}$