Question

What is CD? Show steps please!

Answer 1

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:

$\dfrac{CD}{3}=\dfrac{8}{CD}$         cross multiply

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

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

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