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.
