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myrzilka [38]
3 years ago
11

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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