first of all I have to admit I took way long to solve this question and I still got the wrong answer. Then thinking about it, none of these questions ask you to solve the answer... they just ask you if the information you have is sufficient. The following hinders on 1 assumption as you'll see. I'm not claiming i'm correct but rather i'm asking the community if it makes sense.
BD= v
DA= y
BC =1
DC=x
CA=z
we want to know if x+y+z=5 (perimeter). we can solve for z using the PT (pythag theorem). Thus x+y+f(xy)=5 where f(xy) is some function of xy that equals z.
statement 1 tells us .5*xv=4*.5xy or xv=4xy. We already know that x^2 +v^2 =1 (PT) so we can solve for x in terms of v and substitute it in the first equation and get x*f(x)=4xy where f(x) is some function of x that equals v. We basically have 2 equations with 2 variables now. this should be enough in formation to solve the question.
statement 2 tells us that y=2x. same principle as statement 1 where you have 2 equations and 2 variables.
thoughts? to solve the problem incorrectly it took me 10mins at least. It took me 2 minutes to deduce this logic. then again I might be wrong :/