fionas school is in the shape of a triangle, with three hallways connecting the corners. fiona enters the building and walks 90 yards through the first hallway to the first corner. then, she walks 60 yards through the second hallway to the second corner.

what are the possible lengths of the third hallway?

between 30 yards and 60 yards
between 30 yards and 90 yards
between 30 yards and 120 yards
between 30 yards and 150 yards

Question

fionas school is in the shape of a triangle, with three hallways connecting the corners. fiona enters the building and walks 90 yards through the first hallway to the first corner. then, she walks 60 yards through the second hallway to the second corner.

what are the possible lengths of the third hallway?

between 30 yards and 60 yards
between 30 yards and 90 yards
between 30 yards and 120 yards
between 30 yards and 150 yards

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": [ "Triangle Inequality Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Inequality Theorem" ] } ## Apply the Triangle Inequality Theorem Using the *Triangle Inequality Theorem* knowledge point $$ \begin{aligned} &x + 60 > 90 \implies x > 30 \ &x + 90 > 60 \implies x > -30 \quad (\text{always true for } x > 0) \ &60 + 90 > x \implies x < 150 \ &30 < x < 150 \end{aligned} $$

between 30 yards and 60 yards

between 30 yards and 90 yards

between 30 yards and 120 yards

between 30 yards and 150 yards

{ "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

Answer: