Alcivious draws a square with a side that measures 5 cm. He dilates the square using a scale factor of 4. What is the ration 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 areas of the dilated square to the original square, we first calculate the area of each square.

1. Calculate the area of the original square:

   • The side length of the original square is 5 cm.
   • Area of the original square \( A_{\text{original}} = \text{side}^2 = 5^2 = 25 \) cm².

2. Dilate the square using a scale factor of 4:

   • The side length of the dilated square is \( 5 \times 4 = 20 \) cm.
   • Area of the dilated square \( A_{\text{dilated}} = \text{side}^2 = 20^2 = 400 \) cm².

3. Calculate the ratio of the areas: \[ \text{Ratio} = \frac{A_{\text{dilated}}}{A_{\text{original}}} = \frac{400}{25} = 16. \]

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