Answer: Choice C) {6, 9, 12}
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Step-by-step explanation:
Something like choice A can't form a triangle because the first two sides add to 6+9 = 15, which is not longer than the third side 15. We need to have x+y > z to be true. The same goes for choice B as well because 3+3 = 6 is too small compared to the third side 7. Choice D is similar to choice A.
In short, we can rule out choices A, B, and D.
The only thing left is choice C. Picking any two sides leads to having that sum be larger than the third side
- 6+9 = 15 which is larger than 12
- 9+15 = 24 which is larger than 6
- 6+15 = 21 which is larger than 9
So the conditions of the triangle inequality theorem work out here, and we have a triangle.