Question

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

What is GB?

Group of answer choices

15 units

10 units

30 units

5 units

Answer 1

GB is 15 units

Explanation:

see the attached figure to better understand the problem

we know that

The Centroid is a point of triangle where all 3 medians intersect

In this problem point G is the centroid of the triangle FDE

FA, EB and DC are medians of the triangle FDE.

Remember that centroid divides the median in 2:1

FA is a is median so FG:GA=2:1.

Find the value of x

`(FG)/(GA)=(2)/(1)\\\\(5x)/(x+9)=(2)/(1)\\\\5x=2x+18\\\\5x-2x=18\\\\3x=18\\\\x=6`

Find the value of GB

GB=2x+3

substitute the value of x

`GB=2(6)+3=15\ units`