Question
A painting measures 15 cm long by 24 cm high. You buy two posters, each showing an enlargement of the painting. The first poster measures 45 cm long by 72 cm high. The second poster measures 97.5 cm long by 156 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 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.
Both posters are accurate representations of the painting.
The first poster is an accurate representation of the painting, but the second poster is not an accurate representation.
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.
Both posters are accurate representations of the painting.
The first poster is an accurate representation of the painting, but the second poster is not an accurate representation.
Answers
GPT-4o mini
To determine which of the posters are accurate representations of the painting, we need to check if the aspect ratios (the ratios of length to height) of the posters match that of the painting.
1. **Aspect ratio of the painting:**
- Length = 15 cm
- Height = 24 cm
- Aspect Ratio = Length / Height = 15 / 24 = 5 / 8
2. **Aspect ratio of the first poster:**
- Length = 45 cm
- Height = 72 cm
- Aspect Ratio = Length / Height = 45 / 72
- We can simplify this:
- 45 ÷ 9 = 5
- 72 ÷ 9 = 8
- Aspect Ratio = 5 / 8
3. **Aspect ratio of the second poster:**
- Length = 97.5 cm
- Height = 156 cm
- Aspect Ratio = Length / Height = 97.5 / 156
- We can simplify this:
- 97.5 ÷ 7.5 = 13
- 156 ÷ 7.5 = 20.8 (which is not an integer)
- To verify simplicity, let’s also convert them to a comparable fraction:
- Finding approximate relations:
- 97.5 / 156 = 0.625
- We can check for simple ratios: when considering 5 / 8 = 0.625, technically 5:8 is ratio, hence 0.625 matches!
Since both posters have the same ratio of 5:8 as the painting, both are accurate representations of the painting.
Therefore, the correct answer is:
**Both posters are accurate representations of the painting.**
1. **Aspect ratio of the painting:**
- Length = 15 cm
- Height = 24 cm
- Aspect Ratio = Length / Height = 15 / 24 = 5 / 8
2. **Aspect ratio of the first poster:**
- Length = 45 cm
- Height = 72 cm
- Aspect Ratio = Length / Height = 45 / 72
- We can simplify this:
- 45 ÷ 9 = 5
- 72 ÷ 9 = 8
- Aspect Ratio = 5 / 8
3. **Aspect ratio of the second poster:**
- Length = 97.5 cm
- Height = 156 cm
- Aspect Ratio = Length / Height = 97.5 / 156
- We can simplify this:
- 97.5 ÷ 7.5 = 13
- 156 ÷ 7.5 = 20.8 (which is not an integer)
- To verify simplicity, let’s also convert them to a comparable fraction:
- Finding approximate relations:
- 97.5 / 156 = 0.625
- We can check for simple ratios: when considering 5 / 8 = 0.625, technically 5:8 is ratio, hence 0.625 matches!
Since both posters have the same ratio of 5:8 as the painting, both are accurate representations of the painting.
Therefore, the correct answer is:
**Both posters are accurate representations of the painting.**