Question

question 1 of 10 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 $AD = 20$ and $CD=4$, substituting these values into the proportion gives $\frac{20}{h}=\frac{h}{4}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{20}{h}=\frac{h}{4}$ results in $h^{2}=20\times4 = 80$.

Step3: Solve for h

Taking the square root of both sides of the equation $h^{2}=80$, we get $h=\sqrt{80}$ (we consider the positive value since $h$ represents a length).

Answer:

D. $\sqrt{80}$