Question

In ΔABC, centroid D is on median AM. AD = x + 3 and DM = 2x - 1. Find AM.

A. 7
B. 5/3
C. 8
D. 3 1/2

Answer 1

Option A

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

`x+3:2x-1 =2:1\\x+3 =2(2x-1)\\x+3=4x-2\\5=3x\\Or x=(5)/(3)`

Hence answer is the length of AM

= AD+DM

=
`x+3+2x-1\\=3x+2\\=3((5)/(3) )+2\\=7`

Option A is the answer

Answer 2

check the picture below