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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Pythagorean Theorem" ], "current_concepts": [ "Pythagorean Theorem", "Right Triangles" ] } ## Identify the given sides of the right triangle $$ \begin{aligned} a &= 44 \ b &= 52 \end{aligned} $$ ## Apply the Pythagorean theorem to find the hypotenuse $$ \begin{aligned} c^2 &= a^2 + b^2 \ c^2 &= 44^2 + 52^2 \ c^2 &= 1936 + 2704 \ c^2 &= 4640 \end{aligned} $$ ## Solve for the hypotenuse $$ \begin{aligned} c &= \sqrt{4640} \ c &= 4\sqrt{290} \approx 68.12 \end{aligned} $$ $4\sqrt{290}$ (or approximately $68.12$) { "elements": [ { "type": "point", "params": [[0, 0]], "properties": { "name": "C", "color": "#583C87", "withLabel": false } }, { "type": "point", "params": [[5.2, 0]], "properties": { "name": "B", "color": "#583C87", "withLabel": false } }, { "type": "point", "params": [[0, 4.4]], "properties": { "name": "A", "color": "#583C87", "withLabel": false } }, { "type": "segment", "params": [[0, 0], [5.2, 0]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } }, { "type": "segment", "params": [[0, 0], [0, 4.4]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } }, { "type": "segment", "params": [[0, 4.4], [5.2, 0]], "properties": { "strokeColor": "#F2557F", "strokeWidth": 3 } }, { "type": "text", "params": [[-0.6, 2.2], "44"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [[2.6, -0.4], "52"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [[2.8, 2.4], "?"], "properties": { "color": "#D92B54" } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

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Explanation:

Identify the given sides of the right triangle

Apply the Pythagorean theorem to find the hypotenuse

Solve for the hypotenuse

Answer: