Question

HELP!!! PLEASE!!! 20 POINTS

Answer 1

ΔAEC and ΔBDC are similar.

Therefore the lengths of sides are in proportion.

D is a midpoint of AC, therefore AC = 2BC.

We have proportion:

`(BC)/(BD)=(AC)/(AE)`

Substitute AC = 2BC and BD = 15:

`(BC)/(15)=(2BC)/(AE)\qquad\text{cross multiply}\\\\(AE)(BC)=(15)(2BC)\qquad\text{divide both sides by} BC\\\\AE=(15)(2)\\\\\boxed{AE=30}`