Question

find the exact value of x

Answer 1

ΔABC and ΔCBD are similar. Therefore we have the proportion:

$\dfrac{AB}{BC}=\dfrac{BC}{BD}\\\\AB=6;\ BC=x;\ BD=2$

Substitute:

$\dfrac{6}{x}=\dfrac{x}{2}$    cross multiply

$(x)(x)=(6)(2)\\\\x^2=12\to x=\sqrt{12}\\\\x=\sqrt{4\cdot3}\\\\x=\sqrt4\cdot\sqrt3\\\\\boxed{x=2\sqrt3}$