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:
[tex]\dfrac{BC}{BD}=\dfrac{AC}{AE}[/tex]
Substitute AC = 2BC and BD = 15:
[tex]\dfrac{BC}{15}=\dfrac{2BC}{AE}\qquad\text{cross multiply}\\\\(AE)(BC)=(15)(2BC)\qquad\text{divide both sides by} BC\\\\AE=(15)(2)\\\\\boxed{AE=30}[/tex]
