Answer: Choice C
{11, 17, 27}
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Step-by-step explanation:
Let's go through the answer choices.
- A) This won't work because 6+18 = 24 which is not larger than the third side 24. The sum of any two sides must be larger than the other side. Refer to the triangle inequality theorem.
- B) 5+16 = 21 is not larger than 22, so we rule this out as well.
- C) We'll come back to this later
- D) We rule this out because 8+15 = 23 is not larger than 24.
Now return back to choice C. Notice how adding any two sides leads to a sum larger than the third side
- 11+17 = 28 is larger than 27
- 11+27 = 38 is larger than 17
- 17+27 = 44 is larger than 11
The three conditions of the triangle inequality theorem are met, so a triangle is possible for choice C.