Triangle A B C is shown with centroid G. Lines are drawn from each point of the triangle through the centroid and to the midpoint of the opposite side to form line segment A D, line segment B E, and line segment C F. The length of line segment D G is x minus 15 and the length of line segment G A is x + 7.
G is the centroid of triangle ABC.

What is the value of x?

What is the length of segment DG?

What is the length of segment AG?

What is the length of segment AD?

Answer:

37

22

44

66

Step-by-step explanation:

the value of x is 37

the length of segment DG is 22 units

The length of segment AG is 44 units

the length of segment AD is 66 units

took it on edg

hope this helps (:

The length from the vertex to the centroid is twice the length from the

centroid to the midpoint of the opposite side.

Reasons:

The known parameters are;

The centroid of ΔABC = Point G

Segments [tex]\overline {AD}[/tex], [tex]\overline {BE}[/tex], and [tex]\overline {CF}[/tex] are the medians of ΔABC

Length of line segments [tex]\overline {DG}[/tex] = x - 15

Length of line segments [tex]\overline {GA}[/tex] = x + 7

Required:

The value of x, and lengths of the segments of median [tex]\overline {AD}[/tex]

The median is divided at the centroid of the triangle to ratio 2:1

[tex]Length \ of \ line \ segment \ \overline{GA} = \dfrac{2}{3} \times \overline{AD}[/tex]

Therefore;

[tex]\overline{AD} = \mathbf{\dfrac{3}{2} \times \overline{GA}}[/tex]

[tex]Length \ of \ line \ segment \ \overline{DG} = \mathbf{\dfrac{1}{3} \times \overline{AD}}[/tex]

Therefore;

[tex]\overline{AD} = 3\times \overline{DG}[/tex]

Which gives;

[tex]\dfrac{3}{2} \times \overline{GA} = 3\times \overline{DG}[/tex]

Therefore;

[tex]\dfrac{3}{2} \times (x + 7) = 3\times (x - 15)[/tex]

3·x + 21 = 6·x - 90

21 + 90 = 6·x - 3·x

111 = 3·x

3·x = 111

[tex]x = \dfrac{111}{3} = 37[/tex]

x = 37

[tex]\overline {DG}[/tex] = x - 15

The length of line segment [tex]\overline {DG}[/tex] = 37 - 15 = 22

[tex]\overline {GA}[/tex] = x + 7

Length of line segment [tex]\overline {GA}[/tex] = 37 + 7 = 44

[tex]\overline {AD}[/tex] = [tex]\overline {DG}[/tex] + [tex]\overline {GA}[/tex]

Therefore;

Length of line segment [tex]\overline {AD}[/tex] = 22 + 44 = 66

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https://brainly.com/question/7698132

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