Use the image to answer the question.

To determine the scale factor used to enlarge the rectangle, we first need to find the areas of both the original rectangle and the square, since it appears that the rectangle was enlarged to fit the dimensions of the square.

The area of the original rectangle is calculated as follows:

\[ \text{Area of rectangle} = \text{length} \times \text{width} = 9 , \text{in} \times 5.4 , \text{in} = 48.6 , \text{in}^2 \]

Next, we calculate the area of the square. Since it looks like the side length of the square is given as 5in (but the problem mentions two sides), we'll take the dimension that is relevant with respect to the square's area.

Assuming the square refers to a shape with equal sides:

\[ \text{Area of square} = \text{side} \times \text{side} = 5 , \text{in} \times 5 , \text{in} = 25 , \text{in}^2 \]

Next, we need the scale factor based on the dimensions of the rectangle related to the dimensions of the square. Generally, to find the scale factor, we look at the ratio of dimensions.

Calculating the scale factor for the lengths:

• Length of enlarged rectangle compared to the square:

\[ \text{Scale factor (length)} = \frac{\text{Length of enlarged rectangle}}{\text{Length of dimension square}} = \frac{9}{5} \]

Calculating the scale factor for the widths:

• Width of enlarged rectangle compared to dimensions of the square:

\[ \text{Scale factor (width)} = \frac{\text{Width of enlarged rectangle}}{\text{Width of dimension square}} = \frac{5.4}{5} \]

Now let's convert these to decimals:

• Scale factor (length) = \( \frac{9}{5} = 1.8 \)
• Scale factor (width) = \( \frac{5.4}{5} = 1.08 \)

To summarize, while the length and width scale factors are different, if you are looking for a common scale factor from rectangle to square, we refer to the overall dimensions:

The overall enlargement factor can be taken as the average of both scale factors, but if only lengthening is considered, then take \( 1.8 \) as dominant.

In cases like these, the enlargements are often approximated based on the longest dimensions:

Thus, the overall scale factor used to enlarge the rectangle is approximately 1.8.