the given figures are similar. state the scale factor of large figure to small figure.

5:2
3:5
5:3
2:5

Question

the given figures are similar. state the scale factor of large figure to small figure.

5:2
3:5
5:3
2:5

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 Similarity" ], "new_concepts": [ "Scale Factor", "Similar Polygons" ], "current_concepts": [ "Triangle Similarity", "Scale Factor", "Similar Polygons" ] } ## Identify corresponding sides of the similar figures Using the **Triangle Similarity** knowledge point $$ \begin{aligned} &\text{Large Figure Sides: } 30, 30, 35 \ &\text{Small Figure Sides: } 18, 18, 21 \ &\text{Corresponding Pairs: } (30, 18), (30, 18), (35, 21) \end{aligned} $$ ## Calculate the scale factor from large to small Using the **Triangle Similarity** knowledge point $$ \begin{aligned} &k = \frac{\text{Large Side}}{\text{Small Side}} \ &k = \frac{30}{18} = \frac{5}{3} \ &k = \frac{35}{21} = \frac{5}{3} \ &\text{Ratio} = 5:3 \end{aligned} $$

(A) 5:2

(B) 3:5

(C) 5:3

(D) 2:5

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Similar Polygons" ] }

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Question

Explanation:

Identify corresponding sides of the similar figures

Calculate the scale factor from large to small

Answer: