To determine which canvases are proportional to the photograph, we need to compare the aspect ratios of the photograph and the potential canvases. The aspect ratio is the ratio of the width to the height.
Firstly, let's find the aspect ratio of the photograph:
- The photograph's dimensions are 4 inches by 5 inches.
- The aspect ratio of the photograph is calculated as follows:
[tex]\[
\text{Aspect Ratio of Photograph} = \frac{\text{Width}}{\text{Height}} = \frac{4}{5} = 0.8
\][/tex]
Secondly, we need to determine the aspect ratios of the canvases provided and check which ones match the photograph’s aspect ratio:
1. Canvas 1: 6 inches by 8 inches
- Aspect ratio:
[tex]\[
\frac{6}{8} = 0.75
\][/tex]
- This aspect ratio is not 0.8.
2. Canvas 2: 8 inches by 10 inches
- Aspect ratio:
[tex]\[
\frac{8}{10} = 0.8
\][/tex]
- This aspect ratio matches the photograph’s aspect ratio of 0.8.
3. Canvas 3: 12 inches by 15 inches
- Aspect ratio:
[tex]\[
\frac{12}{15} = 0.8
\][/tex]
- This aspect ratio matches the photograph’s aspect ratio of 0.8.
4. Canvas 4: 16 inches by 20 inches
- Aspect ratio:
[tex]\[
\frac{16}{20} = 0.8
\][/tex]
- This aspect ratio matches the photograph’s aspect ratio of 0.8.
Based on the aspect ratios, the canvases that are proportional to the photograph are:
- 8 inches by 10 inches
- 12 inches by 15 inches
- 16 inches by 20 inches
Finally, we look at the prices of these proportional canvases:
- The canvas with dimensions 8 inches by 10 inches has a price of \[tex]$11.65.
- The canvas with dimensions 12 inches by 15 inches has a price of \$[/tex]18.47.
- The canvas with dimensions 16 inches by 20 inches has a price of \[tex]$22.80.
Therefore, the prices of the canvases that the artist could select are:
\[
\$[/tex] 11.65, \[tex]$ 18.47, \$[/tex] 22.80
\]
The canvases at these prices are proportional to the photograph.
