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. Ivan draws a scale drawing of the same car. His ratio of scale drawing length to actual car length is 2 cm :1 m. What is the length of the car in Ivan’s scale drawing?
The correct answer and explanation is:
To find the length of the car in Ivan’s scale drawing, we need to:
Step 1: Understand Megan’s scale
Megan’s scale is 3 cm : 2 m, which means:
- Every 3 cm in her drawing represents 2 meters in real life.
She draws the car to be 6 cm long.
To find the actual length of the car: 6 cm3 cm=2(twice the scale)\frac{6 \text{ cm}}{3 \text{ cm}} = 2 \quad \text{(twice the scale)}
So the actual car length is: 2×2 m=4 m2 \times 2 \text{ m} = 4 \text{ m}
Step 2: Use Ivan’s scale
Ivan uses a scale of 2 cm : 1 m, which means:
- Every 1 meter of the real car is represented by 2 cm in the drawing.
The actual car length is 4 meters, so in Ivan’s scale: 4 m×2 cm/m=8 cm4 \text{ m} \times 2 \text{ cm/m} = 8 \text{ cm}
✅ Final Answer:
8 cm
🧠 Explanation (300 words):
Scale drawings are representations of real objects, drawn proportionally smaller or larger than the actual object using a specific ratio. In this problem, Megan and Ivan both drew the same car, but with different scale ratios.
Megan’s scale is 3 cm : 2 m, meaning that for every 3 centimeters in her drawing, the actual object is 2 meters long. Since her drawing of the car is 6 cm, we compare this to the scale: 6÷3=2,6 \div 3 = 2,
so the car is drawn at twice the scale length, meaning the actual car is: 2×2 m=4 m.2 \times 2 \text{ m} = 4 \text{ m}.
Now that we know the real car is 4 meters long, we can use Ivan’s scale of 2 cm : 1 m. This ratio means that for every meter of the actual car, Ivan draws 2 centimeters. So: 4 m×2 cm/m=8 cm.4 \text{ m} \times 2 \text{ cm/m} = 8 \text{ cm}.
Thus, Ivan’s drawing of the car should be 8 cm long.
This problem highlights how proportions work in scale drawings. By comparing each scale to the real-life measurement and keeping consistent units, we can move from one person’s drawing to another’s, or to the actual object.