Question

Use the image to answer the 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:
\[
\text{The ratio of the areas is } 16:1
\]