Respuesta :

InesWalston

Answer-

[tex]\boxed{\boxed{GB=15\ units}}[/tex]

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,

[tex]\Rightarrow FG:AG=2:1[/tex]

[tex]\Rightarrow \dfrac{FG}{AG}=\dfrac{2}{1}[/tex]

[tex]\Rightarrow FG=2\times AG[/tex]

[tex]\Rightarrow 5x=2\times (x+9)[/tex]

[tex]\Rightarrow 5x=2x+18[/tex]

[tex]\Rightarrow 3x=18[/tex]

[tex]\Rightarrow x=6[/tex]

So, GB will be [tex]2(6)+3=15[/tex] units

Answer:  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

[tex]FG:GA=2:1\\\\\\\Rightarrow \dfrac{FG}{GA}=\dfrac{2}{1}\\\\\\\Rightarrow \dfrac{5x}{x+9}=2\\\\\\\Rightarrow 5x=2x+18\\\\\Rightarrow 3x=18\\\\\Rightarrow x=6.[/tex]

Therefore, the length of GB will be

[tex]GB=2x+3=2\times6+3=12+3=15~\textup{units}.[/tex]

Thus, the length of GB is 15 units.

Option (C) is correct.

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