Answer:
[tex]\large\boxed{CD=2\sqrt6\ cm}[/tex]
Step-by-step explanation:
ΔDAC and ΔDCB are similar (AA). Therefore the sides are in proportion:
[tex]\dfrac{CD}{DA}=\dfrac{DB}{CD}[/tex]
We have DA = 3cm and DB = 8 cm. Substitute:
[tex]\dfrac{CD}{3}=\dfrac{8}{CD}[/tex] cross multiply
[tex]CD^2=(3)(8)[/tex]
[tex]CD^2=24\to CD=\sqrt{24}[/tex]
[tex]CD=\sqrt{4\cdot6}\\\\CD=\sqrt4\cdot\sqrt6\\\\CD=2\sqrt6\ cm[/tex]
