the legend on a map states that 1 cm is 15 km. if you measure 12 cm on the map, how many km would the actual distance be?

? km

Question

the legend on a map states that 1 cm is 15 km. if you measure 12 cm on the map, how many km would the actual distance be?

?  km

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Dimensional Analysis", "Unit Conversion", "Cross Multiplication" ], "new_concepts": [ "Map Scale Calculations" ], "current_concepts": [ "Dimensional Analysis", "Unit Conversion", "Cross Multiplication", "Map Scale Calculations" ] } ## Identify the given scale and measurement Using the *Dimensional Analysis* and *Unit Conversion* knowledge points $$ \begin{aligned} &\text{Scale ratio: } \frac{15\text{ km}}{1\text{ cm}}\ &\text{Measured distance: } 12\text{ cm} \end{aligned} $$ ## Set up the proportion to solve for the actual distance Using the *Cross Multiplication* knowledge point $$ \begin{aligned} &\frac{1\text{ cm}}{15\text{ km}} = \frac{12\text{ cm}}{x\text{ km}}\ &1 \cdot x = 12 \cdot 15\ &x = 180 \end{aligned} $$ The legend on a map states that $1\text{ cm}$ is $15\text{ km}$. If you measure $12\text{ cm}$ on the map, how many km would the actual distance be? 180 km { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Map Scale Calculations" ] }

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Question

Explanation:

Identify the given scale and measurement

Set up the proportion to solve for the actual distance

Answer: