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?

Let's solve the problem step by step.

### Step 1: Define the variables
Let the width of the rectangular garden be \( w \) feet.

Since the length is 8 feet longer than the width, the length can be expressed as:
\[
l = w + 8
\]

### Step 2: Write the equation for the perimeter
The perimeter \( P \) of a rectangle is given by the formula:
\[
P = 2l + 2w
\]

Substituting the given perimeter (208 feet) and the expression for the length:
\[
208 = 2(w + 8) + 2w
\]

### Step 3: Solve for \( w \)
First, expand and simplify the equation:
\[
208 = 2w + 16 + 2w
\]
\[
208 = 4w + 16
\]
Subtract 16 from both sides:
\[
192 = 4w
\]
Divide by 4:
\[
w = 48 \text{ feet}
\]

### Step 4: Find the length \( l \)
Now that we have \( w = 48 \) feet, substitute it into the expression for the length:
\[
l = 48 + 8 = 56 \text{ feet}
\]

### Step 5: Calculate the area
The area \( A \) of the rectangle is given by:
\[
A = l \times w = 56 \times 48
\]
\[
A = 2688 \text{ square feet}
\]

Thus, the area of the garden is **2688 square feet**.

Would you like further details or have any questions?

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Here are some related questions:
1. What would be the perimeter if the width was increased by 4 feet?
2. How does the area change if both the length and width are doubled?
3. What is the diagonal length of the garden?
4. How would you calculate the width if the perimeter was given as a different value?
5. What if the length was only 5 feet longer than the width, what would be the new area?
6. How do you find the width if the area and perimeter are both given?
7. What are the length and width if the perimeter was 300 feet but the same relationship between length and width was maintained?
8. How does changing the width affect the overall perimeter if the relationship between length and width remains the same?

**Tip:** For any rectangle, doubling one side while keeping the other side constant will double the area.

Learn how to calculate the area of a rectangular garden when given its perimeter of 208 feet and the relationship between its length and width. Follow a step-by-step solution involving algebraic equations and geometric formulas.

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