Megan creates a scale drawing of a car. The ratio of her scale drawing length to actual car
length is 3 cm: 2 m. The length of the car in her drawing is 6 cm.<\/p>\n\n\n\n
Ivan draws a scale drawing of the same car. His ratio of scale drawing length to actual car<\/p>\n\n\n\n
length is 2 cm :1 m.<\/p>\n\n\n\n
What is the length of the car in Ivan’s scale drawing?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To find the length of the car in Ivan’s scale drawing, we need to establish the relationship between the lengths in the scale drawings and the actual length of the car based on their respective ratios.<\/p>\n\n\n\n Step 1: Understand Megan’s Scale Drawing<\/strong><\/p>\n\n\n\n Megan’s ratio of scale drawing length to actual car length is given as (3 \\text{ cm} : 2 \\text{ m}). This means for every 3 cm in her drawing, the actual length of the car is 2 m.<\/p>\n\n\n\n We can convert the actual length from meters to centimeters for easier comparison. Since 1 m equals 100 cm, 2 m becomes:<\/p>\n\n\n\n [ Now, we can express the relationship in the following way:<\/p>\n\n\n\n [ Step 2: Find the Actual Length of the Car<\/strong><\/p>\n\n\n\n According to the problem, the length of the car in Megan’s drawing is 6 cm. Using the ratio we established:<\/p>\n\n\n\n [ To find the actual length, we can set up a proportion:<\/p>\n\n\n\n [ Calculating this gives:<\/p>\n\n\n\n [ Dividing both sides by 3:<\/p>\n\n\n\n [ Step 3: Understand Ivan’s Scale Drawing<\/strong><\/p>\n\n\n\n Ivan’s ratio of scale drawing length to actual car length is (2 \\text{ cm} : 1 \\text{ m}). Converting 1 m to cm gives us:<\/p>\n\n\n\n [ So Ivan’s ratio is (2 \\text{ cm} : 100 \\text{ cm}), which simplifies to:<\/p>\n\n\n\n [ Step 4: Calculate the Length of Ivan’s Drawing<\/strong><\/p>\n\n\n\n Using the same proportion method as before, we can set up the relationship for Ivan:<\/p>\n\n\n\n [ Setting this up as a proportion:<\/p>\n\n\n\n [ Calculating gives:<\/p>\n\n\n\n [ Thus,<\/p>\n\n\n\n [ Conclusion<\/strong><\/p>\n\n\n\n The length of the car in Ivan’s scale drawing is 8 cm<\/strong>. This solution illustrates how to apply ratios to find corresponding lengths in scale drawings, emphasizing the importance of unit conversion and proportional reasoning in practical applications.<\/p>\n","protected":false},"excerpt":{"rendered":" Megan creates a scale drawing of a car. The ratio of her scale drawing length to actual carlength is 3 cm: 2 m. The length of the car in her drawing is 6 cm. Ivan draws a scale drawing of the same car. 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2 \\text{ m} = 2 \\times 100 \\text{ cm} = 200 \\text{ cm}
]<\/p>\n\n\n\n
\\frac{\\text{Drawing length}}{\\text{Actual length}} = \\frac{3 \\text{ cm}}{200 \\text{ cm}}
]<\/p>\n\n\n\n
\\frac{6 \\text{ cm}}{\\text{Actual length}} = \\frac{3 \\text{ cm}}{200 \\text{ cm}}
]<\/p>\n\n\n\n
6 \\text{ cm} \\cdot 200 \\text{ cm} = 3 \\text{ cm} \\cdot \\text{Actual length}
]<\/p>\n\n\n\n
1200 \\text{ cm} = 3 \\cdot \\text{Actual length}
]<\/p>\n\n\n\n
\\text{Actual length} = \\frac{1200 \\text{ cm}}{3} = 400 \\text{ cm}
]<\/p>\n\n\n\n
1 \\text{ m} = 100 \\text{ cm}
]<\/p>\n\n\n\n
\\frac{2 \\text{ cm}}{100 \\text{ cm}} = \\frac{1}{50}
]<\/p>\n\n\n\n
\\frac{\\text{Drawing length}}{400 \\text{ cm}} = \\frac{2 \\text{ cm}}{100 \\text{ cm}}
]<\/p>\n\n\n\n
\\text{Drawing length} \\cdot 100 = 2 \\cdot 400
]<\/p>\n\n\n\n
\\text{Drawing length} \\cdot 100 = 800
]<\/p>\n\n\n\n
\\text{Drawing length} = \\frac{800}{100} = 8 \\text{ cm}
]<\/p>\n\n\n\n