7. 16
8. 8
9. 8
10. 12
11. 12
12. 18
Step-by-step explanation:
The centroid cuts each median into parts in the ratio 2:1. This fact can be used to find the desired lengths.
7. SH = 2/3×SM = 2/3×24 = 16
8. HM = 1/3×SM = 1/3×24 = 8
9. TH = 2×DH = 2×4 = 8
10. HR = 2×EH = 2×6 = 12
11. TD = TH +DH = 8 +4 = 12
12. ER = EH +HR = 6 +12 = 18