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Example Question #561 : Geometry
All of the following could be the possible side lengths of a triangle EXCEPT:
Possible Answers:
Correct answer:
Explanation:
The length of the third side of a triangle must always be between (but not equal to) the sum and the difference of the other two sides.
For instance, take the example of 2, 6, and 7.
and
. Therefore, the third side length must be greater than 4 and less than 8. Because 7 is greater than 4 and less than 8, it is possible for these to be the side lengths of a triangle.
The 5, 7, 12 answer choice is the only option for which this is not the case.
and
. Therefore, the third side length must be between 2 and 12. Because it is equal to the sum, not less than the sum, it is not possible that these could be the side lengths of a triangle.
David
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