Answer:
GH = 18
CH = 6sqrt5
Explanation:
To find GH, we can use the proportional relationship that GH/12 = 12/8
Therefore, GH/12 = 3/2 and GH = 18.
Now to find CH, we can first find BC and then use the Pythagorean theorem.
To find BC, we can use the proportional relationship that GB/BC = BC/BH
Now plugging in the known values, we find that 8/BC = BC/10, so BC^2 = 80 and BC = 4*sqrt5.
Now using Pythagorean Theorem: CH^2 = BH^2 + BC^2
CH^2 = 100 + 80 = 180 —> CH = sqrt180 = 6*sqrt5.
Hope this helps!