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.

Question

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

Answer 1

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

1. Calculate the area of the original square: \[ \text{Area of original square} = \text{side}^2 = 5^2 = 25 \text{ cm}^2 \]

2. Calculate the new side length of the dilated square using the scale factor: \[ \text{New side} = \text{original side} \times \text{scale factor} = 5 \times 4 = 20 \text{ cm} \]

3. Calculate the area of the dilated square: \[ \text{Area of dilated square} = \text{new side}^2 = 20^2 = 400 \text{ cm}^2 \]

4. Find the ratio of the area of the dilated square to the area of the original square: \[ \text{Ratio} = \frac{\text{Area of dilated square}}{\text{Area of original square}} = \frac{400}{25} = 16 \]

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

Therefore, the final answer is: \[ \text{The ratio of the areas is } 16:1. \]