Question

How do I find the answers to 17, 19, and 20?

Answer 1

Answer:

17. 6

18. 18 (as shown)

19. 10/3 = 3 1/3

20. 20/3 = 6 2/3

Step-by-step explanation:

17. For this, you can subtract the given length GB=12 from the length you found for problem 18, BF=18. Doing that tells you FG = 18-12 = 6, as you have marked on the diagram.

19. As with median BF, the point G divides it into two parts that have the ratio 1:2. The distance from G to D is the shorter of the distances, so you have ...

... GD = (1/3) CD = (1/3)·10 = 10/3

... GD = 3 1/3

20. You can subtract GD from CD to get CG, or you can multiply CD by 2/3. The result is the same either way.

... CG = CD -GD = 10 -3 1/3

... CG = 6 2/3

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Comment on centroid and median

The centroid (G) divides each median into parts in the ratio 1:2. Hence the shorter of those parts is half the length of the longer one, or 1/3 the total length of the median.

The longer of the parts is double the length of the shorter one, or 2/3 the total length of the median.

Your marking of median BF seems to show an understanding of these relationships. (Total length: 18; length of parts: 6 and 12.)