Make believe you have a 12 inch stick and a 3 inch stick nailed together at one end (loose enough to be able to pivot).
How big a stick would you need to connect the other ends of the 12 and 3 inch sticks.
If the 3 inch stick is laying on top of the 12 inch stick you'd need just a 9 inch stick. But to make the combination a triangle the third stick would have to be a little bigger than 9 inches.
If the 3 inch stick is rotated 180º so it's collinear with the 12 inch stick but not laying on top of it, you'd now need a 15 inch stick to connect the ends. But to make the combination a triangle the third stick would have to be a little smaller than 15 inches.
So the third stick's length has to be constrained to: 9 < BA < 15.
Both D and E satisfy the constraints.
12/7/2013

Steve S.