Even though I solved it in 5-6 minutes using similar triangles but I don't think we gonna face these problems on real GMAT. If you are, then its almost certain you scored 50-51 in quant.
When you say about similar triangles you mean the rule:
(the area of the bigger triangle) is the same with (the area of the small triangle) x (the squared ratio of their legs) ??
This is the rule I applied: In similar triangles, ratio of the sides is constant.
1/AC = BD/CD = CD/AD and then I applied what is written in two statements.
SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008