To find the total cost of fencing the square vegetable patch as a function of the length of a side $x$, let's break it down step by step.

Step 1: Identify the cost for each side

• East and West sides: There are 2 sides (east and west) with a cost of $7 per foot. The total cost for these two sides is: $2 \times 7x = 14x \, \text{dollars}$

• North and South sides: There are 2 sides (north and south) with a cost of $5 per foot. The total cost for these two sides is: $2 \times 5x = 10x \, \text{dollars}$

Step 2: Total cost function

To find the total cost $C(x)$, we sum the costs for all four sides: $C(x) = 14x + 10x = 24x$ Thus, the total cost of the fencing as a function of the side length $x$ is: $C(x) = 24x \, \text{dollars}$

This function gives you the total fencing cost based on the side length $x$ of the square vegetable patch.

Do you want more details or have any questions?

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Here are 5 related questions you might want to explore:

1. How does the cost change if only one side's cost changes?
2. What happens to the total cost if you change the shape from square to rectangular?
3. How much will the total cost be if the side length $x = 10$ feet?
4. If the total fencing budget is $480, what is the maximum side length you can afford?
5. What if the costs per foot are different for each side? How would you express the function?

Tip: Always double-check units when calculating costs to ensure accuracy.