Question

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

Answer 1

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

Explanation:

Look at the picture.

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

`(AB)/(AC)=(AD)/(AB)`

We have:

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

Substitute:

`(x)/(16)=(5)/(x)` cross multiply

`x^2=(16)(5)\to x=√((16)(5))` use √ab = √a · √b

`x=√(16)\cdot\sqrt5\\\\x=4\sqrt5`