determine which of the following sets of measures can be side lengths of a triangle. select all that apply.

a. 4, 4, 7
b. 2, 9, 12
c. 3, 5, 8
d. 10, 12, 15

Question

determine which of the following sets of measures can be side lengths of a triangle. select all that apply.

a. 4, 4, 7
b. 2, 9, 12
c. 3, 5, 8
d. 10, 12, 15

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Inequality Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Inequality Theorem" ] } ## Apply the Triangle Inequality Theorem to each option $$ \begin{aligned} &\text{For A: } 4 + 4 = 8 > 7 \quad (\text{Valid}) \ &\text{For B: } 2 + 9 = 11 < 12 \quad (\text{Invalid}) \ &\text{For C: } 3 + 5 = 8 gtr 8 \quad (\text{Invalid}) \ &\text{For D: } 10 + 12 = 22 > 15 \quad (\text{Valid}) \end{aligned} $$ ## Identify the valid sets of side lengths $$ \text{Valid options: A and D} $$

(A) 4, 4, 7

(B) 2, 9, 12

(C) 3, 5, 8

(D) 10, 12, 15

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

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QUESTION IMAGE

Question

Explanation:

Apply the Triangle Inequality Theorem to each option

Identify the valid sets of side lengths

Answer: