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in Geometry by (15.8k points)
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In the given figure, A is the midpoint of YZ and G is the centroid of the triangle XYZ. If the length of GA is 3 cm, find XA.

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Best answer

Given A is the midpoint of YZ.

∴ ZA = AY

G is the centroid of ΔXYZ centroid divides each median in a ratio 2 : 1 ⇒ XG : GA = 2 : 1

XG/GA = 2/1

XG/3 = 2/1

XG = 2 × 3

XG = 6 cm

XA = XG + GA

= 6 + 3 ⇒ XA = 9 cm

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