Bis the midpoint of ac, d is the midpoint of ce. bd=10, and ae =2x. find the length of ce if cd =3x

There is a theorem that states that the line joining two midpoints in a triangle is always parallel to the third side and its length is half the length of the third side.

Since B is midpoint of AC and D is midpoint of CE, therefore, BD is parallel to AE and BD = 0.5 AE
AE = 2 BD = 2 x 10 = 2x
Therefore, x= 10

D is the midpoint of CE and CD = 3x, therefore CE = 6x where x = 10
Based on this, CE = 6 x 10 = 60 units of length