Question

G is the centroid of triangle ABC. Find (GD), l(EG) and (AG). (BG) = 6 cm , (GC) = 9cm , (FG) = 5cm

Answer 1

hi dear

The centroid of a triangle divides each median in the ratio 2:1.  i. Point G is the centroid and seg CR is the median. ∴ l(GC) × 1 = 2 × 2.5  ∴ l(GC) = 5  ii. Point G is the centroid and seg BQ is the median. ∴ 6 × 1 = 2 × l(GQ)  ∴ 6/2 = l(GQ)  ∴ 3 = l(GQ)  i.e. l(GQ) = 3  Now, l(BQ) = l(BG) + l(GQ)  ∴ l(BQ) = 6 + 3  ∴ l(BQ) = 9  iii. Point G is the centroid and seg AP is the median.  ∴ l(AG) = 2 l(GP) …..(i) Now, l(AP) = l(AG) + l(GP) … (ii)  ∴ l(AP) = 2l(GP) + l(GP) … [

From (i)]  ∴ l(AP) = 3l(GP)  ∴ 6 = 3l(GP) ...[∵ l(AP) = 6]  ∴ 6/3 = l(GP)  ∴ 2 = l(GP) i.e. l(GP) = 2  l

(AP) = l(AG) + l(GP) …[from (ii)]  ∴ 6 = l(AG) + 2  ∴ l(AG) = 6 – 2  l(AG) = 4

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