Book 6 Chapter 5: Impact of changing the Base on a Triangle

[elan.jones]

Chapter 5 problem set question 2:

Things I understand:
1) Since both triangles are contained within rectangle ABCD they have equal heights
2) If one Line AD as the base for triangle APD and Line AR as the base for triangle AQR the area of Triangle APD will be twice the area of triangle AQR because the base of APD IN THIS CASE is twice the base of AQR
3) The answer should be C: the quantities are equal

What I don't understand:
1) One of the strategies is to test how changing the numbers used in the formula changes the outcome (try to prove D)
2) If you change the either triangle so there is no longer a relationship between the two triangles (for example make the base of triangle APD line AP and the base of triangle AQR line AQ) although the triangles will still share the same height, there is no longer any other relationship between the values of the bases (right?) so no comparison can be made so the answer should be D.

What step am I missing or where is my logic inaccurate?
Thanks!

[tommywallach]

Hey Elan,

I'm afraid I don't understand your question. The back of the book is simply saying that you shouldn't assume the answer is D just because a question doesn't give you any numbers. Often, you can put in your own numbers to see what happens. And, as with any QC question, your goal is always to PROVE d with numbers. However, if you plug in numbers here, you see that the answer is indeed C, as you said. That's what the book says as well, so I'm not sure where you're getting D.

-t

P.S. You can't simply "remove" the constraint that says R is the midpoint.