Question

what is the value of h in the figure below? in this diagram, △bad ~ △cbd.

Explanation:

Step1: Use property of similar triangles

Since $\triangle BAD\sim\triangle CBD$, we have the proportion $\frac{AD}{BD}=\frac{BD}{CD}$. Given $AD = 20 - 4=16$ and $CD = 4$. Let $BD = h$. Then $\frac{16}{h}=\frac{h}{4}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{16}{h}=\frac{h}{4}$ gives us $h^{2}=16\times4$.

Step3: Solve for h

$h^{2}=64$, so $h = 8$ (we take the positive value since $h$ represents a length).

Answer:

E. 8