To determine the scale factor used to enlarge the picture, we need to compare the initial dimensions of the picture (width and length) with the enlarged dimensions.
### Step-by-Step Solution:
1. Initial Dimensions:
- Width: 7 inches
- Length: 9 inches
2. Enlarged Dimensions:
- Width: 31.5 inches
- Length: 40.5 inches
3. Calculate the Scale Factor for Width:
The scale factor for the width can be found by dividing the enlarged width by the initial width:
[tex]\[
\text{Scale factor for width} = \frac{31.5}{7}
\][/tex]
4. Calculate the Scale Factor for Length:
Similarly, the scale factor for the length is found by dividing the enlarged length by the initial length:
[tex]\[
\text{Scale factor for length} = \frac{40.5}{9}
\][/tex]
5. Verify the Scale Factors:
Both the width and length scale factors should be the same if the picture was enlarged proportionally.
Given the results:
- [tex]\(\frac{31.5}{7} = 4.5\)[/tex]
- [tex]\(\frac{40.5}{9} = 4.5\)[/tex]
Since both calculations give the same scale factor, we can confirm that the correct scale factor used to enlarge the picture is [tex]\(4.5\)[/tex].
### Answer:
The correct answer is:
[tex]\[
\frac{31.5}{7}
\][/tex]
This corresponds to the scale factor [tex]\(4.5\)[/tex].
