In triangle JKL, MN is parralle JK. Find NK.?

Question

http://aycu34.webshots.com/image/15233/2002010938149364466_rs.jpg

Answer 1

8/28=12/x
so 8x=28*12
x=(28*12)/8=42
So nk=42

Answer 2

METHOD 1:

Because MN || JK, we get that LMN ~ LJK. This means that:

LM/LJ = LN/LK = MN/JK

We already know the ratio of similitude, being: LM/LJ = 8/36 = 2/9, so we can find LK quite easily:

2/9 = 12/LK
2LK = 108
LK = 54

LK - LN = NK
54 - 12 = 42

Thus, NK = 42

METHOD 2

LJ and LK are cut by parallel lines, thus producing equal ratio segments, being: LM/MJ = LN/NK.
We know LM to be 8 and LN to be 12. We get MJ = LJ - LM = 36 - 8 = 28. Thus:

8/28 = 12/NK
8NK = 28*12
NK = 28*12/8
NK = 14*3 = 42