Abcd is a trapezoid. e is the midpoint of cd and f is the midpoint of ab. find the length of bc and show your work. if cd is 24, what is the length of ce. explain how you calculate your answer.

Let 

AB = 2x 

CD = 2y 

BC = h 

Then for AFED 

y^2 = x^2 + (16 - 12)^2 

y^2 = x^2 + 16 (1) 

For BCEF 

y^2 = x^2 + (12 - h)^2 (2) 

Equating equations (1) and (2) 

x^2 + (12 - h)^2 = x^2 + 16 

(12 - h)^2 = 16 

h^2 - 24h + 144 = 16 

h^2 - 24 + 128 = 0 

(h - 16)(h - 8) = 0 

h = 16 , 8 

h = 16 is obviously not a solution 

Hence BC = 8 

CD = 2CE 

24 = 2CE 

CE = 12