https://file.aiquickdraw.com/mathbot/file/1728423146389282rp7ji.jpg

The problem in the image asks to find the perimeter of a rectangle after it undergoes a dilation with a scale factor of \( \frac{1}{4} \).

### Given:
- Original dimensions of the rectangle:
  - Length = 12 inches
  - Width = 4 inches
- Scale factor = \( \frac{1}{4} \)

### Step 1: Find the new dimensions
The dilation with a scale factor of \( \frac{1}{4} \) will reduce each dimension by that factor.
- New length = \( \frac{1}{4} \times 12 = 3 \) inches
- New width = \( \frac{1}{4} \times 4 = 1 \) inch

### Step 2: Calculate the perimeter
The formula for the perimeter of a rectangle is:
\[
P = 2 \times (\text{length} + \text{width})
\]
Substitute the new dimensions:
\[
P = 2 \times (3 + 1) = 2 \times 4 = 8 \text{ inches}
\]

### Final Answer:
The perimeter of the image after the dilation is **8 inches**.

Would you like further details on how dilation works or any related topics?

### Related Questions:
1. How would the area of the rectangle change after the dilation?
2. What happens to the perimeter if the scale factor is \( \frac{1}{2} \) instead of \( \frac{1}{4} \)?
3. How does the scale factor affect shapes that are not rectangles, like circles or triangles?
4. If the original rectangle had a diagonal of 13 inches, what would the diagonal be after the dilation?
5. Can a dilation increase the size of a shape? What would the perimeter be if the scale factor were 2?

### Tip:
When working with dilations, always remember that the scale factor applies uniformly to all dimensions of the shape, and it directly affects both perimeter and area differently!

The rectangle shown below undergoes a dilation with a scale factor of 1/4. What is the perimeter of the image?

Learn how to calculate the perimeter of a rectangle after it undergoes dilation with a scale factor of 1/4. This problem involves using the perimeter formula for a rectangle and applying the scale factor to find the new dimensions. Suitable for students in Grades 6-8.

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