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3 years ago

What is CD? Show steps please!

Mathematics

1 answer:

Romashka [77]3 years ago

4 0

Answer:

$\large\boxed{CD=2\sqrt6\ cm}$

Step-by-step explanation:

ΔDAC and ΔDCB are similar (AA). Therefore the sides are in proportion:

$\dfrac{CD}{DA}=\dfrac{DB}{CD}$

We have DA = 3cm and DB = 8 cm. Substitute:

$\dfrac{CD}{3}=\dfrac{8}{CD}$ <em>cross multiply</em>

$CD^2=(3)(8)$

$CD^2=24\to CD=\sqrt{24}$

$CD=\sqrt{4\cdot6}\\\\CD=\sqrt4\cdot\sqrt6\\\\CD=2\sqrt6\ cm$

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(a)

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