Mathematics

Problem

In triangle

ABC

, two segments

DE

and

FG

are drawn parallel to

BC

such that

A,F,D

are in this order on

AB

and

A,G,E

are in this order on

AC

. If

AB = 18\,\text{cm}

AF = 6\,\text{cm}

and

AC = 24\,\text{cm}

, find the length of

AG

. a)

12\,\text{cm}

6\,\text{cm}

8\,\text{cm}

16\,\text{cm}