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Use the image to answer the question.



An illustration shows two rectangles. The first is horizontally positioned lengthwise and the second is positioned slanting lengthwise to the left. The first rectangle has a base length of 5 inches and vertical width of 3 inches. The tilted second rectangle has a length of 9 inches and a width of 5.4 inches.
What scale factor was used to enlarge the rectangle in the image? The measurements refer to inches. Give your answer as a decimal.

1 answer

To find the scale factor used to enlarge the rectangle, we need to compare the lengths of the corresponding dimensions of the original rectangle and the enlarged rectangle.

First, let's identify the dimensions of the two rectangles:

  • Original rectangle:

    • Length: 5 inches
    • Width: 3 inches

  • Enlarged rectangle:

    • Length: 9 inches
    • Width: 5.4 inches

Now, we calculate the scale factor for both the length and the width.

  1. Scale factor for length: \[ \text{Scale factor} = \frac{\text{Length of enlarged rectangle}}{\text{Length of original rectangle}} = \frac{9}{5} = 1.8 \]

  2. Scale factor for width: \[ \text{Scale factor} = \frac{\text{Width of enlarged rectangle}}{\text{Width of original rectangle}} = \frac{5.4}{3} = 1.8 \]

Both calculations yield a scale factor of 1.8.

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