Question

Find the exact value of x

Answer 1

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

`(AB)/(BC)=(BC)/(BD)\\\\AB=6;\ BC=x;\ BD=2`

Substitute:

`(6)/(x)=(x)/(2)` cross multiply

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