Rowen uses a scale factor of 1.5 to make a scale drawing of a square. How does the area of the scale drawing compare to that of the original square? Write your answer in decimal form.(1 point)

Question

The area of the scale drawing is __ times the area of the original.

Answer 1

To determine how the area of the scale drawing compares to that of the original square, we start with the following:

1. Let the side length of the original square be \( s \).

2. The area of the original square can be calculated as: \[ \text{Area}_{\text{original}} = s^2 \]

3. When Rowen uses a scale factor of \( 1.5 \), the side length of the scale drawing becomes: \[ \text{Side length}_{\text{scale}} = 1.5s \]

4. The area of the scale drawing can then be calculated as: \[ \text{Area}_{\text{scale}} = (1.5s)^2 = 2.25s^2 \]

5. To find how the area of the scale drawing compares to that of the original, we take the ratio of the areas: \[ \text{Ratio} = \frac{\text{Area}{\text{scale}}}{\text{Area}{\text{original}}} = \frac{2.25s^2}{s^2} = 2.25 \]

Thus, the area of the scale drawing is \( 2.25 \) times the area of the original square.

In decimal form:

The area of the scale drawing is 2.25 times the area of the original.