Great question. Can anybody give the answer and explanation?

If the triangle was (equilateral or isosceles or AD=DC) then BD/AB = Sin60 and DC/BC=Cos60. So Choice A. but
it is not mentioned in question. so it could be any triangle hence Choice D.

Let's sketch some diagrams that CONFORM to the given information (triangle with perpendicular line drawn from top vertex)

Here's one:

In this diagram, BD is much shorter than AB, so BD/AB is a small number that's pretty close to 0.
Also, we can see that DC and BC are close to having the same length. So, DC/BC is pretty close to 1
So, in this instance, Quantity B is greater.



Here's another diagram:

In this diagram, BD and AB are close to having the same length. So BD/AB is probably between 0.5 and 1
Also, we can see that DC is much shorter than BC, so DC/BC is a small number that's pretty close to 0
So, in this instance, Quantity A is greater.

Answer:
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No other information except BD and AC is perpendicular.

Multiple possibilities arise as we don't know anything about the triangle. And can't define anything from only this 90 degree. Therefore, D is the right answer.