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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem" ] } ## Identify the given side lengths $$ \begin{aligned} a &= 44 \ b &= 52 \end{aligned} $$ ## Apply the Pythagorean theorem $$ \begin{aligned} c^2 &= a^2 + b^2 \ c^2 &= 44^2 + 52^2 \ c^2 &= 1936 + 2704 \ c^2 &= 4640 \end{aligned} $$ ## Solve for the hypotenuse $$ \begin{aligned} c &= \sqrt{4640} \ c &= 4\sqrt{290} \approx 68.12 \end{aligned} $$ $4\sqrt{290}$ (or approximately $68.12$) { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

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Explanation:

Identify the given side lengths

Apply the Pythagorean theorem

Solve for the hypotenuse

Answer: