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Question

One smaller and one larger square side by side.

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 first need to calculate the areas of both squares.

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

2. Dilated square: The side of the dilated square can be calculated by multiplying the side of the original square by the scale factor: \[ \text{side}_{\text{dilated}} = 5 \text{ cm} \times 4 = 20 \text{ cm} \]

   Now, calculate the area of the dilated square: \[ \text{Area}{\text{dilated}} = \text{side}{\text{dilated}}^2 = 20^2 = 400 \text{ cm}^2 \]

3. Ratio of the areas: Now, we find the ratio of the area of the dilated square to the area of the original square: \[ \text{Ratio} = \frac{\text{Area}{\text{dilated}}}{\text{Area}{\text{original}}} = \frac{400}{25} = 16 \]

Thus, the ratio of the areas is: \[ \text{The ratio of the areas is } 16:1 \]