Three Answers:
Choice B
Choice D
Choice E
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Step-by-step explanation:
Use the triangle inequality theorem. This is the idea where adding any two sides must lead to a result larger than the third side; otherwise, a triangle is not possible. I recommend cutting out strings of paper of these lengths to confirm that you can make a triangle or not.
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For choice A, a triangle is not possible since the first two sides add to 1+1 = 2, but this isn't larger than the third side of 2 units. All we can do really is just form a straight line and not a triangle. We can rule choice A out.
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Choice B is a triangle. Specifically it is a 3-4-5 right triangle that is famous with the pythagorean theorem. Note how...
- 3+4 = 7 is larger than 5
- 4+5 = 9 is larger than 3
- 3+5 = 8 is larger than 4
so adding any two sides of this triangle leads to the sum being larger than the third remaining side. Choice B is one of the answers.
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Choice C is not a triangle. We have 5+5 = 10 but that isn't larger than 11. We can rule this out.
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Choice D is a triangle since
- 7+8 = 15 is larger than 12
- 7+12 = 19 is larger than 8
- 8+12 = 20 is larger than 7
any two sides sum to a value larger than the third side
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Choice E is a triangle. We have an equilateral triangle with all sides the same length, and all angles the same value (60 degrees). This is another answer.
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Choice F is similar to choice C. We have the first two sides add to something smaller than the third side (4+8 = 12 is smaller than 13). We can rule this out.