Problem 7
Lets go through the answer choices for this one
Choice A)
Notice how 11+11 = 22 is smaller than 24
The sum of the first two sides must be larger than the third side for a triangle to form. We come up short in this case
So we rule out choice C
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Choice B)
18+12 = 30 is larger than 9
12+9 = 21 is larger than 18
18+9 = 27 is larger than 12
Because we can pick any two sides, add them up, and the result is larger than the other third side this means that a triangle is possible for choice B
So this is the correct answer
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Choie C is eliminated since 10+9 = 19 is not larger than 19
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Similarly, we can rule choice D out because 4+7 = 11 is not larger than 23
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Problem 8
c = missing side
a = 9
b = 15
b-a < c < b+a
15-9 < c < 15+9
6 < c < 24
so the third missing side is between 6 and 24 (excluding both endpoints)
In other words, the missing side is larger than 6 and smaller than 24
You have the correct answer here as well. Nice work on both problems.