Sure! Let's go through the problem step-by-step:
1. Determine the initial dimensions of the rectangle:
- The length of the rectangle is 6 cm.
- The width of the rectangle is 5 cm.
2. Calculate the initial area of the rectangle:
- The area [tex]\( A \)[/tex] of a rectangle is given by the formula [tex]\( A = \text{length} \times \text{width} \)[/tex].
- Substituting the given dimensions:
[tex]\[
A_{\text{initial}} = 6 \, \text{cm} \times 5 \, \text{cm} = 30 \, \text{cm}^2
\][/tex]
3. Identify the new area of the rectangle after enlargement:
- The new area is given as 270 cm².
4. Calculate the area scale factor:
- The area scale factor tells us how many times larger the new area is compared to the initial area.
- The area scale factor [tex]\( k \)[/tex] can be found using the formula:
[tex]\[
k = \frac{\text{new area}}{\text{initial area}}
\][/tex]
- Substituting the values we have:
[tex]\[
k = \frac{270 \, \text{cm}^2}{30 \, \text{cm}^2} = 9.0
\][/tex]
Therefore, the area scale factor is 9.0.
