Respuesta :

Answer:

Basically G is centeroid (intersection point all three medians) so it divides BD in the ratio of 2:1

if bd is x then 2x/3 = BG i.e 38

so GD is x/3 i.e 19

Answer:  The correct option is (A) 19.

Step-by-step explanation:  We are to find the length of DG in the triangle shown in the figure, where BG = 38 units.

From the figure, we see that

the point G is the centroid of triangle ABC. Also, the centroid of a triangle divides each of the three medians in the ratio 2 : 1.

So, for the median BD, we get

[tex]BG:DG=2:1\\\\\Rightarrow \dfrac{BG}{DG}=\dfrac{2}{1}\\\\\Rightarrow \dfrac{38}{DG}=2\\\\\Rightarrow DG=\dfrac{38}{2}\\\\\Rightarrow DG=19.[/tex]

Thus, the required length of DG is 19 units.

Option (A) is CORRECT.

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