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:

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.

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