Problem 16
Answer: Choice B) 21, 8, 10
This is because the two smaller sides 8 and 10 add to 8+10 = 18, but this is not greater than the side 21. For a triangle to be possible, the sum of any two sides must be larger than the third side. I recommend cutting out slips of paper of these lengths to confirm that a triangle is indeed not possible in this case.
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Problem 17
Answer: Choice B) 10, 15, 22
Choice A is not the answer because 13+8 = 21, but that's not larger than the third side 21.
Choice C is not the answer because 6+11 = 17 which is not larger than 24.
Choice B is the only possible answer. Note we have the three following true inequalities
- 15+22 > 10
- 10+22 > 15
- 10+15 > 22
So adding any two sides of this triangle leads to a sum larger than the third side. We're using the triangle inequality theorem.