IMC 2004 — Keystage 3 (IWYMIC) — individual Question 3

In triangle $ABC$, $AB=30$ cm, $AC=32$ cm. Points $D,E,F,G$ lie respectively on $AB,AC,AD,AE$, so that $BCD,CDE,DEF,EFG,FGA$ have equal areas. Find $FD$ in centimetres.