Answer:
B. 8
Step-by-step explanation:
Triangles ADB, ABC and BDC are similar.
Therefore, we can use ratios to find BD.
Using the ratio of the long leg to the short leg of ΔBDC and ΔADB:
[tex]\dfrac{BD}{16}=\dfrac{4}{BD}[/tex]
Cross multiply and solve for BD:
[tex]\implies BD^2=4 \times 16[/tex]
[tex]\implies BD^2=64[/tex]
[tex]\implies BD=\sqrt{64}[/tex]
[tex]\implies BD=8[/tex]
