如图，AB∥GH∥CD，点H在BC上，AC与BD交于点G，AB=2，CD=3，则GH的长为．

Question

如图，AB∥GH∥CD，点H在BC上，AC与BD交于点G，AB=2，CD=3，则GH的长为______．

Answer 1

∵AB∥GH，
∴(GH)/(AB)=(CH)/(BC)，即(GH)/(2)=(CH)/(BC)①，
∵GH∥CD，
∴(GH)/(CD)=(BH)/(BC)，即(GH)/(3)=(BH)/(BC)②，
①+②，得(GH)/(2)+(GH)/(3)=(CH)/(BC)+(BH)/(BC)=(BC)/(BC)=1，
∴(GH)/(2)+(GH)/(3)=1，
解得GH=(6)/(5)．
故答案为(6)/(5)．