optional | mathematics review

* $c

Question

optional | mathematics review

* $c < a + b$

given the line segments with measurements $a$, $b$ and $c$, is it possible to make a triangle?

1. $a = 4, b = 5, c = 7$

2. $a = 2, b = 4, c = 7$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Triangle Inequality Theorem" ], "current_concepts": [ "Triangle Inequality Theorem" ] } ## Check the first set of side lengths $$ \begin{aligned} &a = 4, \quad b = 5, \quad c = 7 \ &a + b = 4 + 5 = 9 > 7 \quad (\text{True}) \ &a + c = 4 + 7 = 11 > 5 \quad (\text{True}) \ &b + c = 5 + 7 = 12 > 4 \quad (\text{True}) \end{aligned} $$ ## Check the second set of side lengths $$ \begin{aligned} &a = 2, \quad b = 4, \quad c = 7 \ &a + b = 2 + 4 = 6 < 7 \quad (\text{False}) \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 1 | $a = 4, b = 5, c = 7$ | Yes | | 2 | $a = 2, b = 4, c = 7$ | No | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Inequality Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Check the first set of side lengths

Check the second set of side lengths

Answer: