I deduced this as the following.
s+t+r+u = 360
r+s = 90 (gn; t+u = 270)
since r = 2s; 3s= 90; s= 30 → r = 60

Now we have two 90-30-60 triangles and we are told to compare the two sides ( or the ratio of them).

ED would be the opposite of angle r (60deg) and AC would the opp side of angle s (30 deg)
→ which would be sqrt(3) * a / a = sqrt(3) which is < 2 ;
So ended up choosing B

But the answer turns out to be A.

Am I missing anything? Help me out. Thanks in advance!

You have correctly deduced that AC is opposite to a 30-degree angle. However, its length would be (a/sqrt(3)) and not a. This is because the ratio AC/AB would be 1/sqrt(3). Similary, the ratio BD/ED would be 1/sqrt(3) as well.

ABC and BED are similar triangles. ED=\sqrt3 BD= \sqrt3 AB, whereas AB=BD= \sqrt3 AC,
hence \frac{ED}{AC} =\frac{\sqrt3AB}{AC}= \frac{\sqrt3 \sqrt3 AC}{AC}=3 .
If ABC and BED are congruent triangles then your method is correct. Need to be careful here.