Question

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.

Answer 1

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