Question

What is CD? Show steps please!

Answer 1

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

Explanation:

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

`(CD)/(DA)=(DB)/(CD)`

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

`(CD)/(3)=(8)/(CD)` cross multiply

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

`CD^2=24\to CD=√(24)`

`CD=√(4\cdot6)\\\\CD=\sqrt4\cdot\sqrt6\\\\CD=2\sqrt6\ cm`