the areas of two similar octagons are $4\text{ m}^2$ and $9\text{ m}^2$. what is the scale factor of their side lengths?

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Question

the areas of two similar octagons are $4\text{ m}^2$ and $9\text{ m}^2$. what is the scale factor of their side lengths?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Area Ratio of Similar Figures", "Scale Factor" ], "new_concepts": [], "current_concepts": [ "Area Ratio of Similar Figures", "Scale Factor", "Similarity Transformations" ] } ## Relate area ratio to scale factor $$ \frac{\text{Area}_1}{\text{Area}_2} = k^2 $$ ## Substitute given areas $$ \frac{4}{9} = k^2 $$ ## Solve for scale factor $$ k = \sqrt{\frac{4}{9}} = \frac{2}{3} $$ The areas of two similar octagons are $4\text{ m}^2$ and $9\text{ m}^2$. What is the scale factor of their side lengths? $2:3$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Area Ratio of Similar Figures" ] }

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QUESTION IMAGE

Question

Explanation:

Relate area ratio to scale factor

Substitute given areas

Solve for scale factor

Answer: