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

side 1: $2x + 10$
side 2: $4x - 2$
side 3: $3x + 5$

yes
no

Question

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

side 1: $2x + 10$
side 2: $4x - 2$
side 3: $3x + 5$

yes
no

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Equiangular Triangle" ], "new_concepts": [], "current_concepts": [ "Equiangular Triangle", "Equilateral Triangle Properties" ] } ## Equate the side lengths of the equiangular triangle An equiangular triangle is also equilateral, meaning all three side lengths must be equal: $$ 2x + 10 = 4x - 2 = 3x + 5 $$ ## Solve for x using two of the expressions $$ \begin{aligned} 2x + 10 &= 4x - 2 \ 12 &= 2x \ x &= 6 \end{aligned} $$ ## Check consistency with the third side length Substitute $x = 6$ into all three expressions to verify if they yield equal, positive side lengths: $$ \begin{aligned} 2(6) + 10 &= 22 \ 4(6) - 2 &= 22 \ 3(6) + 5 &= 23 \end{aligned} $$ Since $22 eq 23$, no single value of $x$ can make all three side lengths equal.

Yes

No

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Equate the side lengths of the equiangular triangle

Solve for x using two of the expressions

Check consistency with the third side length

Answer: