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 the poster be similar to the painting?)
The first poster is an accurate representation of the painting, but the second poster is not an accurate representation.
Both posters are accurate representations of the painting.
Both posters are not accurate representations of the painting.
The first poster is not an accurate representation of the painting, but the second poster is an accurate representation.
The first poster is an accurate representation of the painting, but the second poster is not an accurate representation.
Both posters are accurate representations of the painting.
Both posters are not accurate representations of the painting.
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 the posters are accurate representations of Van Gogh's painting "Starry Night," we need to check whether the aspect ratios of the posters match the aspect ratio of the painting.
The aspect ratio is calculated as the width divided by the height.
For the painting "Starry Night":
- Dimensions: 92 cm (length) by 73 cm (height)
- Aspect ratio = 92 / 73
Calculating the aspect ratio:
\[
\text{Aspect ratio of the painting} = \frac{92}{73} \approx 1.26
\]
Now let's calculate the aspect ratios for the posters:
**First poster:**
- Dimensions: 120 cm (length) by 100 cm (height)
\[
\text{Aspect ratio of the first poster} = \frac{120}{100} = 1.2
\]
**Second poster:**
- Dimensions: 138 cm (length) by 109.5 cm (height)
\[
\text{Aspect ratio of the second poster} = \frac{138}{109.5} \approx 1.26
\]
Now we compare the aspect ratios:
- The aspect ratio of the painting (approximately 1.26) matches the aspect ratio of the second poster (approximately 1.26).
- The aspect ratio of the first poster (1.2) does not match the aspect ratio of the painting.
Therefore, the conclusion is:
- The first poster is not an accurate representation of the painting, but the second poster is an accurate representation.
Thus, the correct answer is:
**The first poster is not an accurate representation of the painting, but the second poster is an accurate representation.**
The aspect ratio is calculated as the width divided by the height.
For the painting "Starry Night":
- Dimensions: 92 cm (length) by 73 cm (height)
- Aspect ratio = 92 / 73
Calculating the aspect ratio:
\[
\text{Aspect ratio of the painting} = \frac{92}{73} \approx 1.26
\]
Now let's calculate the aspect ratios for the posters:
**First poster:**
- Dimensions: 120 cm (length) by 100 cm (height)
\[
\text{Aspect ratio of the first poster} = \frac{120}{100} = 1.2
\]
**Second poster:**
- Dimensions: 138 cm (length) by 109.5 cm (height)
\[
\text{Aspect ratio of the second poster} = \frac{138}{109.5} \approx 1.26
\]
Now we compare the aspect ratios:
- The aspect ratio of the painting (approximately 1.26) matches the aspect ratio of the second poster (approximately 1.26).
- The aspect ratio of the first poster (1.2) does not match the aspect ratio of the painting.
Therefore, the conclusion is:
- The first poster is not an accurate representation of the painting, but the second poster is an accurate representation.
Thus, the correct answer is:
**The first poster is not an accurate representation of the painting, but the second poster is an accurate representation.**