Let #G# be the centroid where medians #AD and BE# meet.
As #AG:GD=BG:GE=2:1#,
let #AG=2y, => GD=y#,
let #BG=2x, => GE=x#
In #DeltaBGD, (2x)^2+y^2=(7/2)^2#
#=> 4x^2+y^2=(49)/4 ----- Eq(1)#
In #DeltaAGE, x^2+(2y)^2=3^2#,
#=> x^2+4y^2=9 ----- Eq(2)#
Adding #Eq(1) and Eq(2)# together, we get:
#5x^2+5y^2=49/4+9#
#=> 5(x^2+y^2)=85/4#
#=> color(red)(x^2+y^2=17/4)#
In #AGB, AB^2=(2x)^2+(2y)^2#
#=> AB^2=4(x^2+y^2)=4*(17)/4=17#
#=> AB=sqrt17# units