Question

In the diagram, GB = 2x + 3..

Triangle F D E has centroid G. Lines are drawn from each point to the midpoint of the opposite side to form line segments F A, D C, E B. The length of line segment F G is 5 x and the length of line segment G A is x + 9.

What is GB?

5 units
10 units
15 units
30 units

Answer 1

10 units

Explanation:

It's important to know that the centroid is always two-thirds of the median. Which means

`AG=(2)/(3)FA\\ x+9=(2)/(3)(5x+x+9)\\ x+9=(2)/(3)(6x+9) \\x+9=4x+6\\9-6=4x-x\\3x=3\\x=1`

Which means
`AG=x+9=1+9=10`.

But, the centroid has always the same distance from each vertex, which means

`AG=BG=10`

Therefore, BG is 10 units long.

Answer 2

it's 15 on edge

Explanation:

basically, you want to solve for x and substitute it for 2x+3,

Solving for x is

5x=2+18

3x=18

x=6

now getting GB

2(6)+3

12+3

15

Hope that helps