Question

Point G is the centroid of triangle ABC. If AP = 6, then AG = □ and GP = □​

Answer 1

Answer:

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) = 4Read more on Sarthaks.com - https://www.sarthaks.com/853607/fill-in-the-blanks-point-g-is-the-centroid-of-abc-i-if-l-rg-5-then-l-gc-ii-if-l-bg-6-then-bq