Answer:
Option A
Step-by-step explanation:
Given that in triangle ABC AM is one median
D is the centroid
We know by triangle conjectures that
in any triangle centroid divides median in the ratio 2:1
i.e. If D is centroid on AM,
then AD:DM =2:1
Substitute for AD and DM the given values
[tex]x+3:2x-1 =2:1\\x+3 =2(2x-1)\\x+3=4x-2\\5=3x\\Or x=\frac{5}{3}[/tex]
Hence answer is the length of AM
= AD+DM
= [tex]x+3+2x-1\\=3x+2\\=3(\frac{5}{3} )+2\\=7[/tex]
Option A is the answer
