In the diagram, gb = 2x + 3.. what is gb? a.5 units b.10 units c.15 units d.30 units

Answer-

Solution-

From the attachment,

AD = AE, so FA is a median.

BD = BF, so BE is a median.

CF = CE, so DC is a median.

And G is the centroid.

From the properties of centroid, we know that

The centroid divides each median in a ratio of 2:1

So,

So, GB will be units

 The correct option is (C) 15 units.

Step-by-step explanation:  We are given to find the length of GB in the figure.

Given that

FG = 5x  and  GA = x + 9.

From the figure, we note that DC, EB and FA are the medians of ΔDEF drawn from the vertices D, E and F respectively.

Since, the medians intersect at the point G, so G is the centroid of ΔDEF.

We know that the centroid divides each median of a triangle in the ratio 2 : 1, so we have

Therefore, the length of GB will be

Thus, the length of GB is 15 units.

Option (C) is correct.