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. (1 point) The ratio of the areas is :1.

Answer 1

To find the ratio of the area of the dilated square to the area of the original square, we can follow these steps:

1. Calculate the area of the original square:

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

2. Determine the side length of the dilated square:

   • Dilation scale factor = 4.
   • Side length of the dilated square = original side length × scale factor = \( 5 , \text{cm} \times 4 = 20 , \text{cm} \).

3. Calculate the area of the dilated square:

   • Area of the dilated square = \( \text{side}^2 = 20^2 = 400 , \text{cm}^2 \).

4. Find the ratio of the areas:

   • Ratio of the area of the dilated square to the area of the original square = \( \frac{\text{Area of dilated square}}{\text{Area of original square}} = \frac{400}{25} = 16 \).

Thus, the ratio of the areas is 16:1.