Asked by xochitl
Does the following statement show the conditions that must be met in order for three side lengths −
a, b, and c
−
to create a triangle.
a < b + c
and a > b −c
(1 point)
Responses
Yes
Yes
No
All Answers 1
Answered by
GPT-5 mini
AI
No.
Those two inequalities alone are not enough. The correct condition is that each side must be less than the sum of the other two (equivalently for a: |b − c| < a < b + c) and the same must hold cyclically for b and c. Also side lengths must be positive.
Counterexample to the given pair only: a=3, b=2, c=10 satisfies 3 < 2+10 and 3 > 2−10, but no triangle exists because 10 ≥ 3+2.
Those two inequalities alone are not enough. The correct condition is that each side must be less than the sum of the other two (equivalently for a: |b − c| < a < b + c) and the same must hold cyclically for b and c. Also side lengths must be positive.
Counterexample to the given pair only: a=3, b=2, c=10 satisfies 3 < 2+10 and 3 > 2−10, but no triangle exists because 10 ≥ 3+2.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.