https://file.aiquickdraw.com/mathbot/file/1725575452968lwl19i6r.jpg

Let's analyze the image and solve the problem step-by-step.

### Given Information:
1. The scale factor is 5.
2. We need to find:
   - The perimeter for the scaled copy.
   - The area of rectangle K (the original rectangle).

### Step 1: Calculate the dimensions of rectangle K
From the grid on the image:
- The height of rectangle K is 6 units (counting the squares vertically).
- The width of rectangle K is 2 units (counting the squares horizontally).

### Step 2: Calculate the perimeter of rectangle K
The formula for the perimeter of a rectangle is:
\[
P = 2 \times (\text{height} + \text{width})
\]
For rectangle K:
\[
P = 2 \times (6 + 2) = 2 \times 8 = 16 \, \text{units}
\]

### Step 3: Calculate the perimeter of the scaled copy
The scale factor is 5. So, the dimensions of the scaled rectangle will be:
- New height = \( 6 \times 5 = 30 \, \text{units} \)
- New width = \( 2 \times 5 = 10 \, \text{units} \)

Now, calculate the perimeter of the scaled rectangle:
\[
P_{\text{scaled}} = 2 \times (30 + 10) = 2 \times 40 = 80 \, \text{units}
\]

### Step 4: Calculate the area of rectangle K
The formula for the area of a rectangle is:
\[
A = \text{height} \times \text{width}
\]
For rectangle K:
\[
A = 6 \times 2 = 12 \, \text{square units}
\]

### Final Answers:
1. **Perimeter for the scaled copy**: 80 units.
2. **Area for rectangle K**: 12 square units.

Let me know if you have any questions or need more details! Here are some related questions to deepen your understanding:

1. How would the area of rectangle K change if the scale factor was different?
2. How is the scale factor applied to the perimeter of the rectangle?
3. What happens to the perimeter if the scale factor is less than 1?
4. How can we find the scale factor if we only know the dimensions of the scaled copy?
5. How does the area of the scaled rectangle relate to the area of the original?

**Tip:** The perimeter scales linearly with the scale factor, but the area scales with the square of the scale factor.

What is the perimeter for the scale copy and the area of rectangle K?

Solve for the perimeter of the scaled copy and the area of rectangle K, given a scale factor of 5. Learn the application of geometric formulas for perimeter and area, suitable for middle school students in Grades 6-8.

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