Question
Van Gogh’s painting Starry Night measures 92 cm long by 73 cm high. You buy two posters, each showing an enlargement of the painting. The first poster measures 120 cm long by 100 cm high. The second poster measures 138 cm long by 109.5 cm high. Which of the following is true? (Hint: To be an accurate representation of the painting, would the poster be similar to the painting?)
Both posters are accurate representations of the painting.
Both posters are not accurate representations of the painting.
The first poster is an accurate representation of the painting, but the second poster is not an accurate representation.
The first poster is not an accurate representation of the painting, but the second poster is an accurate representation.
Both posters are accurate representations of the painting.
Both posters are not accurate representations of the painting.
The first poster is an accurate representation of the painting, but the second poster is not an accurate representation.
The first poster is not an accurate representation of the painting, but the second poster is an accurate representation.
Answers
GPT-4o mini
To determine whether each poster is an accurate representation of Van Gogh's painting "Starry Night," we need to check if the aspect ratios (the ratio of length to height) of the posters match the aspect ratio of the painting.
1. **Calculate the aspect ratio of the original painting:**
- Length: 92 cm
- Height: 73 cm
- Aspect Ratio = Length / Height = 92 / 73
2. **Calculate the aspect ratio of the first poster:**
- Length: 120 cm
- Height: 100 cm
- Aspect Ratio = 120 / 100 = 1.2
3. **Calculate the aspect ratio of the second poster:**
- Length: 138 cm
- Height: 109.5 cm
- Aspect Ratio = 138 / 109.5 = 1.26 (approximately)
Now we can compute the aspect ratio of the original painting:
- Original Aspect Ratio = 92 / 73 ≈ 1.26027
Now we can compare:
- **First Poster Aspect Ratio:** 1.2
- **Second Poster Aspect Ratio:** 1.26 (approximately)
When comparing these ratios:
- The first poster (1.2) does not match the painting's aspect ratio (~1.26027).
- The second poster (1.26) is close to the original aspect ratio (approximately 1.26027), effectively similar enough to be considered an accurate representation.
Thus, the final answer is:
**The first poster is not an accurate representation of the painting, but the second poster is an accurate representation.**
1. **Calculate the aspect ratio of the original painting:**
- Length: 92 cm
- Height: 73 cm
- Aspect Ratio = Length / Height = 92 / 73
2. **Calculate the aspect ratio of the first poster:**
- Length: 120 cm
- Height: 100 cm
- Aspect Ratio = 120 / 100 = 1.2
3. **Calculate the aspect ratio of the second poster:**
- Length: 138 cm
- Height: 109.5 cm
- Aspect Ratio = 138 / 109.5 = 1.26 (approximately)
Now we can compute the aspect ratio of the original painting:
- Original Aspect Ratio = 92 / 73 ≈ 1.26027
Now we can compare:
- **First Poster Aspect Ratio:** 1.2
- **Second Poster Aspect Ratio:** 1.26 (approximately)
When comparing these ratios:
- The first poster (1.2) does not match the painting's aspect ratio (~1.26027).
- The second poster (1.26) is close to the original aspect ratio (approximately 1.26027), effectively similar enough to be considered an accurate representation.
Thus, the final answer is:
**The first poster is not an accurate representation of the painting, but the second poster is an accurate representation.**