Answer:
[tex]\large\boxed{A:\ 4\sqrt5}[/tex]
Step-by-step explanation:
Look at the picture.
ΔABC and ΔADB are similar. The corresponding angles are in proportion:
[tex]\dfrac{AB}{AC}=\dfrac{AD}{AB}[/tex]
We have:
[tex]AB=x,\ AC=5+11=16,\ AD=5[/tex]
Substitute:
[tex]\dfrac{x}{16}=\dfrac{5}{x}[/tex] cross multiply
[tex]x^2=(16)(5)\to x=\sqrt{(16)(5)}[/tex] use √ab = √a · √b
[tex]x=\sqrt{16}\cdot\sqrt5\\\\x=4\sqrt5[/tex]
