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G is the centroid of triangle ABC.What is the value of x? What is the length of segment DG? unitsWhat is the length of segment AG? unitsWhat is the length of segment AD? units

G Is The Centroid Of Triangle ABCWhat Is The Value Of X What Is The Length Of Segment DG UnitsWhat Is The Length Of Segment AG UnitsWhat Is The Length Of Segmen class=

Sagot :

A centroid is the point of intersection of the 3 medians of a triangle. Each median connects the the midpoint of each side to the vertex opposite it. This means that lines AD, BE and CF are medians of the triangle.

Recall, a centroid divides each median in the ratio of 2:3 or 2/3

Considering median AD, it means that

DG/AG = 2/3

From the diagram,

DG = x - 15

AG = x + 7

Thus,

(x - 15)/(x + 7) = 2/3

By crossmultiplying, we have

3(x - 15) = 2(x + 7)

We would open the parentheses by multiplying the terms inside it by the the term outside. Thus, we have

3x - 45 = 2x + 14

3x - 2x = 14 + 45 = 59

x = 59

The length of segment DG = x - 15 = 59 - 15 = 44

The length of segment AG = x + 7 = 59 + 7 = 66

The length of segment AD = DG + AG = 44 + 66 = 110

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