College

An architect made a scale model of a building. The dimensions of the scale model are shown below.

The front of the actual building is 80 feet wide. Which proportion compares the measurements of the model to the actual building?

[tex]
\[
\begin{array}{l}
\frac{24}{80} = \frac{12}{40} \\
\frac{24}{80} = \frac{9}{12} \\
\frac{9}{80} = \frac{24}{30}
\end{array}
\]
[/tex]

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].