Question

Answers are A:4 square root 5 B:16 C:6 D:8 square root 5

Answer 1

Answer:

$\large\boxed{A:\ 4\sqrt5}$

Step-by-step explanation:

Look at the picture.

ΔABC and ΔADB are similar. The corresponding angles are in proportion:

$\dfrac{AB}{AC}=\dfrac{AD}{AB}$

We have:

$AB=x,\ AC=5+11=16,\ AD=5$

Substitute:

$\dfrac{x}{16}=\dfrac{5}{x}$                 cross multiply

$x^2=(16)(5)\to x=\sqrt{(16)(5)}$         use √ab = √a · √b

$x=\sqrt{16}\cdot\sqrt5\\\\x=4\sqrt5$