Points M and N are marked on the sides AC and BC of triangle ABC, respectively, so that triangle AMN

Points M and N are marked on the sides AC and BC of triangle ABC, respectively, so that triangle AMN is similar to triangle ABC find AN if AM = 5 BM = 9 AC = 7

Since the tracks are similar. we can make a proportion:
AM: AB = AN: AC
5: (9 + 5) = AN: 7
5: 14 = AN: 7
14AN = 5 * 7
2AN = 5
AN = 5/2
AN = 2.5
Answer: 2.5