Let's walk through the problem step by step to determine what should be the correct dimensions of Beth's card after applying the scale factor.
1. Initial dimensions of the card:
- Length: 6 inches
- Width: 3 inches
2. Scale factor:
- The provided scale factor is [tex]\(\frac{2}{3}\)[/tex].
3. Applying the scale factor:
- The scale factor is a reduction since [tex]\(\frac{2}{3}\)[/tex] is less than 1.
- To find the new dimensions, we multiply the initial dimensions by the scale factor.
[tex]\[
\text{New Length} = 6 \, \text{inches} \times \frac{2}{3} = 4 \, \text{inches}
\][/tex]
[tex]\[
\text{New Width} = 3 \, \text{inches} \times \frac{2}{3} = 2 \, \text{inches}
\][/tex]
4. Verification of current card dimensions:
- The print shop gave Beth a card measuring 9 inches by 13.5 inches.
- Comparing this to the initial dimensions multiplied by the scale factor, the print shop's dimensions are incorrect.
5. Correct dimensions of the card:
- The calculations show that after applying the scale factor of [tex]\(\frac{2}{3}\)[/tex], the correct dimensions of the card should be:
[tex]\[
\text{Length} = 4 \, \text{inches}
\][/tex]
[tex]\[
\text{Width} = 2 \, \text{inches}
\][/tex]
Thus, the correct dimensions of the card should be 4 inches by 2 inches, confirming that the first option is correct:
The correct answer is:
The scale factor is a reduction, and the new card should be 4 inches by 2 inches.
