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Serggg [28]
3 years ago
8

Find the exact value of x

Mathematics
1 answer:
tresset_1 [31]3 years ago
6 0

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}    <em>cross multiply</em>

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

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