https://file.aiquickdraw.com/mathbot/file/1725923959415mviupd7k.jpg

The problem in the image relates to how dimensions, perimeter, and area change during dilations (scaling). Let's break it down:

1. **Perimeter** changes by the **scale factor**.
2. **Area** changes by the **square of the scale factor**.
3. To determine the new area or perimeter, you typically **multiply** by the scale factor.

Now, filling in the blanks:

- When changing dimensions in dilations, the perimeter changes by the **scale factor** and the area changes by the **scale factor squared**.
- To determine the new area or perimeter, you **multiply** by the scale factor.

Would you like more details or have any further questions?

Here are five related questions to expand understanding:
1. How does the volume change when scaling a 3D object by a scale factor?
2. What happens to the perimeter if the scale factor is less than 1?
3. How would you calculate the new area if the scale factor is 3?
4. Can the perimeter remain unchanged during a dilation? If so, under what conditions?
5. How is the concept of dilation applied in real-world problems like map scaling or models?

**Tip**: Always remember that area is affected by the square of the scale factor, while the perimeter is affected only by the scale factor itself.

When changing dimensions in dilations, the perimeter changes by the Scale Factor and the area changes by the Scale Factor Squared. To determine the new area or perimeter, you multiply by the Scale Factor.

Explore how dilations affect the perimeter and area of geometric shapes. Learn that the perimeter changes by the scale factor, while the area changes by the square of the scale factor. Perfect for Grades 7-9 students, this problem explains the concept of scaling and includes step-by-step solutions.

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