are the expressions for the side lengths possible for this equiangular triangle?

yes
no

Question

are the expressions for the side lengths possible for this equiangular triangle?

yes
no

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Equilateral Triangle Properties" ], "new_concepts": [], "current_concepts": [ "Equilateral Triangle Properties", "Linear Equations" ] } ## Equate side lengths Using the *Equilateral Triangle Properties* knowledge point $$ \begin{aligned} &14x - 4 = 4x + 1\ &10x = 5\ &x = 0.5 \end{aligned} $$ ## Verify consistency of the third side Using the *Equilateral Triangle Properties* knowledge point $$ \begin{aligned} &\text{Side 1: } 14(0.5) - 4 = 7 - 4 = 3\ &\text{Side 2: } 4(0.5) + 1 = 2 + 1 = 3\ &\text{Side 3: } 12(0.5) - 3 = 6 - 3 = 3 \end{aligned} $$ ## Determine possibility Using the *Equilateral Triangle Properties* knowledge point $$ \begin{aligned} &\text{All three sides are equal to } 3.\ &\text{Since } 3 > 0\text{, these side lengths are geometrically possible.} \end{aligned} $$

Yes

No

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Equilateral Triangle Properties" ] }

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QUESTION IMAGE

Question

Explanation:

Equate side lengths

Verify consistency of the third side

Determine possibility

Answer: