Quant Group 9 Flash Cards Q15

Could you explain why the heights for Triangle ABC and Triangle BCE are the same in this question. I understand the bases are the same but the heights are throwing me off.

I have been having trouble with this question as I would assume the heights are different based on how a potential triangle CDE would be set up. As AB and CD would be the same heights, then CE would be a hypotenuse, making it different from AB.

Feel free to explain it by starting from the beginning when approaching this problem. Thanks!

XE is the height of triangle BCE. What is the relationship between XE and AB?