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The length of a rectangular garden is 8 feet longer than its width. If the garden's perimeter is 208 feet, what is the area of the garden in square feet?

To solve the problem in the image, we need to find the perimeter of the figure made of two rectangles in terms of \( p \) and then simplify the expression.

### Given:
- The figure is composed of two rectangles.
- The dimensions of the rectangles are given in terms of \( p \):
  - **Left Rectangle**: \( 7p \times 7p \)
  - **Right Rectangle**: \( 14p \times (7p + 8) \)

### Steps to Find the Perimeter:
1. **Identify the lengths of all the sides of the figure:**
   - The left side: \( 7p \)
   - The right side: \( 14p \)
   - The top side (combination of the top sides of both rectangles): \( 7p + 8 \)
   - The bottom side: \( 7p \) (from the left rectangle)
   - The middle side (from the bottom of the right rectangle to the top of the left rectangle): \( 8 \)

2. **Add all the sides to find the perimeter:**
   - The perimeter \( P \) is the sum of all the outer sides:
   \[
   P = 7p + 14p + (7p + 8) + 7p + 8 + 14p
   \]

3. **Simplify the expression:**
   - Combine like terms:
   \[
   P = (7p + 14p + 7p + 14p) + (8 + 8)
   \]
   - Simplify further:
   \[
   P = (7p + 7p + 14p + 14p) + 16 = 42p + 16
   \]

### Final Answer:
The perimeter of the figure in terms of \( p \) is \( \boxed{42p + 16} \).

Would you like any further details or explanations? Here are some related questions to consider:

1. What is the area of the entire figure in terms of \( p \)?
2. How would the perimeter change if the width of the second rectangle were doubled?
3. What if the height of the first rectangle were increased by a factor of 2?
4. If the height of the second rectangle were \( 14p - 5 \), how would the perimeter change?
5. Can you express the area of the two rectangles separately in terms of \( p \)?
6. How would the problem change if both rectangles were squares?
7. What if you added another rectangle of width \( 7p \) and height \( 7p + 8 \)?
8. How would the perimeter be affected if the two rectangles were rearranged?

**Tip:** When finding the perimeter of a composite shape, it helps to carefully track each side's contribution to ensure no length is overlooked or double-counted.

Discover how to calculate the area of a rectangular garden when its perimeter is known. This problem involves understanding the relationship between the dimensions of the garden and applying geometric formulas. Suitable for students in Grades 7-9.

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