in $\delta lmn$, $\angle l$ is obtuse. which is the largest side length?

* $\overline{mn}$
* $\overline{ln}$
* $\overline{nl}$
* $\overline{lm}$

Question

in $\delta lmn$, $\angle l$ is obtuse. which is the largest side length?

* $\overline{mn}$
* $\overline{ln}$
* $\overline{nl}$
* $\overline{lm}$

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": [ "Angle-Side Relationship" ], "new_concepts": [], "current_concepts": [ "Angle-Side Relationship", "Triangle Classification" ] } ## Identify the largest angle in the triangle Using the *Angle-Side Relationship* knowledge point $$ \begin{aligned} &\text{In } \triangle LMN, \angle L \text{ is obtuse } (\angle L > 90^\circ).\ &\text{Since the sum of angles in a triangle is } 180^\circ:\ &\angle M + \angle N = 180^\circ - \angle L < 90^\circ.\ &\text{Therefore, } \angle L \text{ is the largest angle in } \triangle LMN. \end{aligned} $$ ## Determine the longest side Using the *Angle-Side Relationship* knowledge point $$ \begin{aligned} &\text{The longest side of a triangle is always opposite the largest angle.}\ &\text{The side opposite to } \angle L \text{ is } \overline{MN}.\ &\text{Thus, } \overline{MN} \text{ is the largest side length.} \end{aligned} $$

(A) $\overline{MN}$

(B) $\overline{LN}$

(C) $\overline{NL}$

(D) $\overline{LM}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Angle-Side Relationship" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the largest angle in the triangle

Determine the longest side

Answer: