Please Answer

This is due by tomorrow night and I need help

AY = 16

IY = 9

FG = 30

PA = 24

Step-by-step explanation:

The centroid of the triangle divides each median at the ratio 1: 2 from the base

Let us solve the problem

In Δ AFT

∵ Y is the centroid

∵ AP, TI, and FG are medians

→ By using the rule above

∴ Y divides AP at ratio 1: 2 from the base FT

∴ AY = 2 YP

∵ YP = 8

∴ AY = 2(8)

∴ AY = 16

∵ PA = AY + YP

∴ AP = 16 + 8

∴ AP = 24

∵ Y divides TI at ratio 1: 2 from the base FA

∴ TY = 2 IY

∵ TY = 18

∴ 18 = 2

→ Divide both sides by 2

∴ 9 = IY

∴ IY = 9

∵ Y divides FG at ratio 1:2 from the base AT

∴ FY = 2 YG

∵ FY = 20

∴ 20 = 2 YG

→ Divide both sides by 2

∴ 10 = YG

∴ YG = 10

∵ FG = YG + FY

∴ FG = 10 + 20

∴ FG = 30