Question

question 9 of 10 what is the value of x in the figure below? in this diagram, △abd ~ △cad.

Explanation:

Step1: Use property of similar triangles

Since $\triangle ABD\sim\triangle CAD$, we have $\frac{BD}{AD}=\frac{AD}{CD}$. Given $BD = 5$ and $CD=9$, and $AD = x$. So, $\frac{5}{x}=\frac{x}{9}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{5}{x}=\frac{x}{9}$ gives us $x^{2}=5\times9 = 45$.

Step3: Solve for x

Taking the square root of both sides of the equation $x^{2}=45$, we get $x=\sqrt{45}$ (we consider the positive value since $x$ represents a length).

Answer:

E. $\sqrt{45}$