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Answer :
To solve the problem, we need to determine which proportion correctly compares the measurements of a scale model and the actual building. Here's how to go about it step-by-step:
1. Identify the Dimensions:
- Width of the model: 24 units
- Width of the actual building: 80 feet
- The problem provides additional information for a height comparison:
- Model height 1: 12 units
- Corresponding actual height 1: 40 units
- Model height 2: 9 units
- Corresponding actual height 2: 30 units
2. Understand the Proportions:
- A proportion means two ratios that are equal to each other.
- We need to check whether the ratios of model dimensions to actual dimensions match.
3. Evaluate Each Option:
- Option 1: [tex]\(\frac{24}{80} = \frac{12}{40}\)[/tex]
- Calculate both sides:
- [tex]\( \frac{24}{80} = 0.3 \)[/tex]
- [tex]\( \frac{12}{40} = 0.3 \)[/tex]
- Both ratios are the same, so this is a correct proportion.
- Option 2: [tex]\(\frac{24}{80} = \frac{9}{12}\)[/tex]
- Calculate both sides:
- [tex]\( \frac{24}{80} = 0.3 \)[/tex]
- [tex]\( \frac{9}{12} = 0.75 \)[/tex]
- These ratios do not match, so this is not a correct proportion.
- Option 3: [tex]\(\frac{9}{80} = \frac{24}{30}\)[/tex]
- Calculate both sides:
- [tex]\( \frac{9}{80} = 0.1125 \)[/tex]
- [tex]\( \frac{24}{30} = 0.8 \)[/tex]
- These ratios do not match, so this is not a correct proportion.
Based on the calculations, the correct proportion that compares the measurements of the model and the actual building is [tex]\(\frac{24}{80} = \frac{12}{40}\)[/tex].
1. Identify the Dimensions:
- Width of the model: 24 units
- Width of the actual building: 80 feet
- The problem provides additional information for a height comparison:
- Model height 1: 12 units
- Corresponding actual height 1: 40 units
- Model height 2: 9 units
- Corresponding actual height 2: 30 units
2. Understand the Proportions:
- A proportion means two ratios that are equal to each other.
- We need to check whether the ratios of model dimensions to actual dimensions match.
3. Evaluate Each Option:
- Option 1: [tex]\(\frac{24}{80} = \frac{12}{40}\)[/tex]
- Calculate both sides:
- [tex]\( \frac{24}{80} = 0.3 \)[/tex]
- [tex]\( \frac{12}{40} = 0.3 \)[/tex]
- Both ratios are the same, so this is a correct proportion.
- Option 2: [tex]\(\frac{24}{80} = \frac{9}{12}\)[/tex]
- Calculate both sides:
- [tex]\( \frac{24}{80} = 0.3 \)[/tex]
- [tex]\( \frac{9}{12} = 0.75 \)[/tex]
- These ratios do not match, so this is not a correct proportion.
- Option 3: [tex]\(\frac{9}{80} = \frac{24}{30}\)[/tex]
- Calculate both sides:
- [tex]\( \frac{9}{80} = 0.1125 \)[/tex]
- [tex]\( \frac{24}{30} = 0.8 \)[/tex]
- These ratios do not match, so this is not a correct proportion.
Based on the calculations, the correct proportion that compares the measurements of the model and the actual building is [tex]\(\frac{24}{80} = \frac{12}{40}\)[/tex].
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