Manhattan Prep Geo Guide - #3 p. 41

[Alexander]

Hi -

I worked through this problem a few times with 2 different strategies . First use BCDF to find BD. Second, use BDEA to find BD and then find FD or BF.

The second method is more complicated and ugly. I only realized this after trying to do it. The first way is much cleaner because if BCDF has a side of 2, knowing 45/45/90 rules you know that BD is radical(2). Squaring radical(2) is much cleaner and easy.

With all that said, how can I pick up on a problem like this that route 1 is easier. I'd hate to waste time and get this wrong since I understand the concepts.

Thanks,
Alexander

[tommywallach]

Hey Alex,

They're both entirely viable, so I really wouldn't worry about it. I don't agree that the first method is significantly harder. If you plug in 2 for the sides of BCDF, the hypotenuse is 2*rt. 2, which is now the length of a side of BDEA, and solving from there is pretty easy.

-t