To determine the total cost of fencing the square vegetable patch, let's break it down:

1. Length of each side: Since the vegetable patch is square, each side has length $x$ feet.

2. Cost for the east and west sides: These two sides cost $6 per foot, and each side is $x$ feet long. Therefore, the total cost for these two sides is: $2 \times 6x = 12x \text{ dollars}.$

3. Cost for the north and south sides: These two sides cost $5 per foot, and each side is $x$ feet long. Therefore, the total cost for these two sides is: $2 \times 5x = 10x \text{ dollars}.$

4. Total cost of the fencing: The total cost is the sum of the costs for all four sides: $\text{Total cost} = 12x + 10x = 22x \text{ dollars}.$

Thus, the total cost $C(x)$ of the fencing as a function of the length $x$ (in feet) of a side is: $C(x) = 22x \text{ dollars}.$

Would you like more details on this or have any further questions?

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Here are 5 related questions:

1. What is the cost if each side of the square is 10 feet long?
2. How would the total cost change if the price for the north and south sides increased to $7 per foot?
3. How much would it cost if the east and west sides were 15 feet long, and the price for the fencing on those sides changed to $8 per foot?
4. What is the total fencing cost if only three sides of the square are fenced, assuming the same prices?
5. How would the cost change if you doubled the size of the vegetable patch?

Tip: When solving word problems, clearly define variables and units early to avoid confusion during calculations!