Let the intersection of the dotted line and BD in the figure be E, and it can be known from the folding mode that AG=GE, and GE is perpendicular to BD.

Area of triangle ABD =3*4/2=6.

Triangle ADG area =AD*AG/2=3AG/2.

BDG area of triangle =DB*AG/2=5AG/2

Triangle ABD area = triangle DAG area+triangle DBG area

Therefore, 3AG/2+5AG/2=6.

AG= 1.5

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