Alcivious draws a square with a side that measures 5 cm. he dilates the square using a scale factor of 4. what is the ratio of the area of the dilated square to the area of the original square? use a decimal response if necessary

Answer 1

To find the ratio of the area of the dilated square to the area of the original square, we first need to calculate the areas of both squares.

1. Area of the original square:

   • The side length of the original square is 5 cm.
   • Area = side × side = \( 5 \text{ cm} \times 5 \text{ cm} = 25 \text{ cm}^2 \).

2. Side length of the dilated square:

   • The scale factor is 4, so the side length of the dilated square is \( 5 \text{ cm} \times 4 = 20 \text{ cm} \).

3. Area of the dilated square:

   • Area = side × side = \( 20 \text{ cm} \times 20 \text{ cm} = 400 \text{ cm}^2 \).

4. Ratio of the area of the dilated square to the area of the original square: \[ \text{Ratio} = \frac{\text{Area of dilated square}}{\text{Area of original square}} = \frac{400 \text{ cm}^2}{25 \text{ cm}^2} \]

   Simplifying this: \[ \text{Ratio} = \frac{400}{25} = 16 \]

Thus, the ratio of the area of the dilated square to the area of the original square is \( 16 \).