Question
A basketball court is 94 feet long. If the image is a scale drawing of a basketball court, which scale factor might the drawing use?
A. 1:400
B. 500:1
C. 1:4
D. 50:1
A. 1:400
B. 500:1
C. 1:4
D. 50:1
Answers
Answered by
GPT-4o mini
To determine which scale factor might be used for the drawing of a basketball court that is 94 feet long, we can evaluate each of the provided scale factors.
1. **A. 1:400**
This means that 1 unit on the drawing represents 400 units in real life. If we take this into account, the corresponding length in the drawing would be:
\[
\text{Length in drawing} = \frac{94 \text{ feet}}{400} \approx 0.235 \text{ feet} \text{ (or about 2.82 inches)}
\]
This is very small and not practical for a basketball court.
2. **B. 500:1**
This means that 1 unit in the drawing represents 500 units in real life. The corresponding length in the drawing would be:
\[
\text{Length in drawing} = \frac{94 \text{ feet}}{500} \approx 0.188 \text{ feet} \text{ (or about 2.26 inches)}
\]
Again, this is very small and not practical.
3. **C. 1:4**
This means that 1 unit on the drawing represents 4 units in real life. The corresponding length in the drawing would be:
\[
\text{Length in drawing} = \frac{94 \text{ feet}}{4} = 23.5 \text{ feet}
\]
This is a reasonable size for a drawing of a basketball court.
4. **D. 50:1**
This means that 1 unit on the drawing represents 50 units in real life. The corresponding length in the drawing would be:
\[
\text{Length in drawing} = \frac{94 \text{ feet}}{50} \approx 1.88 \text{ feet} \text{ (or about 22.56 inches)}
\]
This is also a reasonable size for a drawing.
Considering the sizes calculated, **C (1:4)** and **D (50:1)** are both practical. However, since the problem asks for "which scale factor might the drawing use?" the **1:4 scale** (C) gives a larger and more reasonable size for practical viewing.
Thus, the most likely answer is:
**C. 1:4**
1. **A. 1:400**
This means that 1 unit on the drawing represents 400 units in real life. If we take this into account, the corresponding length in the drawing would be:
\[
\text{Length in drawing} = \frac{94 \text{ feet}}{400} \approx 0.235 \text{ feet} \text{ (or about 2.82 inches)}
\]
This is very small and not practical for a basketball court.
2. **B. 500:1**
This means that 1 unit in the drawing represents 500 units in real life. The corresponding length in the drawing would be:
\[
\text{Length in drawing} = \frac{94 \text{ feet}}{500} \approx 0.188 \text{ feet} \text{ (or about 2.26 inches)}
\]
Again, this is very small and not practical.
3. **C. 1:4**
This means that 1 unit on the drawing represents 4 units in real life. The corresponding length in the drawing would be:
\[
\text{Length in drawing} = \frac{94 \text{ feet}}{4} = 23.5 \text{ feet}
\]
This is a reasonable size for a drawing of a basketball court.
4. **D. 50:1**
This means that 1 unit on the drawing represents 50 units in real life. The corresponding length in the drawing would be:
\[
\text{Length in drawing} = \frac{94 \text{ feet}}{50} \approx 1.88 \text{ feet} \text{ (or about 22.56 inches)}
\]
This is also a reasonable size for a drawing.
Considering the sizes calculated, **C (1:4)** and **D (50:1)** are both practical. However, since the problem asks for "which scale factor might the drawing use?" the **1:4 scale** (C) gives a larger and more reasonable size for practical viewing.
Thus, the most likely answer is:
**C. 1:4**