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8_murik_8 [283]
3 years ago
6

In triangle ACE, P is the centroid, PF = 6 , and AD = 15 15. Find the measures of PC and AP. Enter your answers as numbers.

Mathematics
1 answer:
xxTIMURxx [149]3 years ago
5 0

Answer:

PC = 12 units

AP = 10 units

Step-by-step explanation:

  • The centroid of a triangle is the intersection of the three medians of the triangle
  • Each median connecting a vertex with the midpoint of the opposite side
  • The centroid divides each median into two parts, which are always in the ratio 2: 1 from the vertex

In ΔACE

∵ P is the centroid of it

∴ P divides CF the ratio 2: 1 from C

∴ PC = 2 PF

∵ PF = 6 units

∴ PC = 2(6)

∴ PC = 12 units

∵ P divides AD at the ratio 2: 1 from A

→ That means AD = 2 + 1 = 3 parts, and AP = \frac{2}{3} AD

∴ AP = \frac{2}{3} AD

∵ AD = 15 units

∴ AP = AP = \frac{2}{3} (15)

∴ AP = 10 units

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