Question

Help please?? 50 points!

Answer 1

$6 \sqrt{3}$
is the correct answer

Answer 2

The triangle ABC and the triangle BCD are similar, therefore

$\dfrac{3+9}{x}=\dfrac{x}{9}\ \ \ |cross\ multiply\\\\x^2=12\cdot9\\\\x^2=108\to x=\sqrt{108}\\\\x=\sqrt{36\cdot3}\\\\x=\sqrt{36}\cdot\sqrt3\\\\\boxed{x=6\sqrt3}$