Answer :

To solve the question, we need to determine the scale factor of the dilation that caused the perimeter of a rectangle to change from 2.5 to 10.

### Step-by-Step Solution:

1. Understanding Perimeter and Dilation:
- The perimeter of a rectangle is the sum of all its sides.
- Dilation in geometry involves resizing a figure by a certain scale factor, which affects all linear dimensions of the figure, including the perimeter.

2. Identifying Initial and Final Perimeters:
- The initial perimeter of the rectangle is given as 2.5.
- The final perimeter of the rectangle after dilation is given as 10.

3. Determining the Scale Factor:
- The scale factor of a dilation can be found by dividing the final measurement by the initial measurement.
- In this context, since we need to determine how much the perimeter increased, we can use the ratio of the final perimeter to the initial perimeter.

4. Calculation:
- We divide the final perimeter (10) by the initial perimeter (2.5):

[tex]\[ \text{Scale Factor} = \frac{\text{Final Perimeter}}{\text{Initial Perimeter}} = \frac{10}{2.5} \][/tex]

5. Obtaining the Scale Factor:
- Performing this division gives:

[tex]\[ \frac{10}{2.5} = 4 \][/tex]

Therefore, the scale factor of the dilation is 4. This means that each linear dimension of the rectangle, including the sides used to calculate the perimeter, was multiplied by 4 during the dilation process.