small square:big square

Question

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 0:1.
Check answer
) Remaining Attempts : 3

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. Calculate the area of the original square:

• The side length of the original square is 5 cm.
• The area of the original square \( A_1 \) is given by the formula: \[ A_1 = \text{side}^2 = 5^2 = 25 \text{ cm}^2. \]

2. Determine the side length of the dilated square:

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

3. Calculate the area of the dilated square:

• The area of the dilated square \( A_2 \) is given by: \[ A_2 = \text{side}^2 = 20^2 = 400 \text{ cm}^2. \]

4. Now, we can find the ratio of the area of the dilated square to the area of the original square: \[ \text{Ratio} = \frac{A_2}{A_1} = \frac{400 \text{ cm}^2}{25 \text{ cm}^2} = 16. \]

Therefore, the ratio of the area of the dilated square to the area of the original square is 16:1.