A square garden is to be fenced using wooden posts five inches wide. These posts five inches wide. These posts are to be placed at a gap one foot ( one foot is twelve inches). If there are 50 wooden posts available and the fences one each side of the garden begin and end with a wooden post , what could be the maximum lenght ( in inches ) of a side of the garden ?

Answer

To find the maximum length of a side of a square garden that can be fenced using wooden posts, we will follow these steps:

### Step 1: Understand the arrangement of posts and gaps
Each side of the garden will have wooden posts placed at intervals of 1 foot (12 inches). Each wooden post is 5 inches wide. The arrangement will look like this: post - gap - post - gap - ... - post.

### Step 2: Determine the total number of posts used on one side
Let \( n \) be the number of gaps between the posts on one side. Since the fence begins and ends with a wooden post, the number of posts on one side will be \( n + 1 \).

### Step 3: Calculate the total number of posts available
We have a total of 50 wooden posts available. Since there are 4 sides to the square garden, the total number of posts used will be \( 4(n + 1) \). Therefore, we have the equation:
\[ 4(n + 1) \leq 50 \]
This simplifies to:
\[ n + 1 \leq 12.5 \]
Since \( n \) must be a whole number, the maximum value for \( n + 1 \) is 12, which means \( n = 11 \).

### Step 4: Calculate the total length of one side of the garden
The total length of one side of the garden can be calculated by considering the width of the posts and the gaps. The total length \( L \) of one side is given by:
\[ L = \text{(number of posts)} \times \text{(width of each post)} + \text{(number of gaps)} \times \text{(width of each gap)} \]
Substituting the values:
- Number of posts on one side = \( n + 1 = 12 \)
- Number of gaps = \( n = 11 \)
- Width of each post = 5 inches
- Width of each gap = 12 inches

Thus, the length of one side is:
\[ L = 12 \times 5 + 11 \times 12 \]
Calculating this:
\[ L = 60 + 132 = 192 \text{ inches} \]

### Conclusion
The maximum length of a side of the garden is **192 inches**.

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