Can you figure this math problem out?

Question

The length of AE is 20 cm. B is the midpoint of AC, C is the midpoint of BD, and D is the midpoint of BE. What is the length of DE in cm?

Here is the link to the picture below.

http://i113.photobucket.com/albums/n218/diamondtrim305/hsg-13.jpg

The one with the best answer and explanation will get earn the points of the Best Answer. By the way it is Geometry. If you know theorems, please use them.

Answer 1

I don't think you need any theorems.

If B is the midpoint of AC, then AB = BC.
If C is the midpoint of BD, then CD = BC = AB (from the last sentence).
If D is the midpoint of BE, then BD = DE. But BD = BC + CD = 2BC = 2AB.

So basically all the lengths are the same except for DE, which is twice as long.

Let x be the length of AB. Then x + x + x + 2x = 20, so 5x = 20, so x = 4. Since they want the length of DE, that's 2(4) = 8.