Find the exact value of x

asked Sep 15, 2019 6.7k views

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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

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

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