To find the perimeter and area of a rectangle and its dilated version, we need the dimensions of the original rectangle (length and width). However, since these dimensions are not provided in your question, I will give you a method on how to calculate these values once you have the dimensions.
Let's denote the original rectangle's length as \( L \) and width as \( W \).
Step 1: Calculate the Perimeter and Area of the Original Rectangle
Perimeter \( P \) of a rectangle is given by the formula: \[ P = 2(L + W) \]
Area \( A \) of a rectangle is given by the formula: \[ A = L \times W \]
Step 2: Calculate the Perimeter and Area of the Dilated Rectangle
When a rectangle is dilated by a scale factor of \( k \) (in this case, \( k = 5 \)):
- The new length will be \( L' = k \times L = 5L \)
- The new width will be \( W' = k \times W = 5W \)
Now we calculate the perimeter and the area of the dilated rectangle.
Perimeter of the dilated rectangle \( P' \) is given by: \[ P' = 2(L' + W') = 2(5L + 5W) = 10(L + W) = 5P \]
Area of the dilated rectangle \( A' \) is given by: \[ A' = L' \times W' = (5L) \times (5W) = 25(L \times W) = 25A \]
Final Summary
- For the original rectangle:
- Perimeter \( P = 2(L + W) \)
- Area \( A = L \times W \)
- For the dilated rectangle:
- Perimeter \( P' = 5P = 10(L + W) \)
- Area \( A' = 25A = 25(L \times W) \)
Once you substitute the values for \( L \) and \( W \) into these formulas, you will obtain the perimeter and area for both the original and dilated rectangles. Please provide the dimensions if you would like me to calculate actual numerical values.