Final answer:
To find the dimensions of the garden that would create the maximum area, use the formula for the perimeter of a rectangle. The dimensions that would create the maximum area are 16 meters by 16 meters. The maximum possible area is 256 square meters.
Step-by-step explanation:
To find the dimensions of the garden that would create the maximum area, we can use the formula for the perimeter of a rectangle, which is 2L + W, where L is the length and W is the width. In this case, we know that the rock wall is one side of the garden, so the length of the garden will be equal to the length of the rock wall.
Using the given information that there are 64 meters of fencing available, we can set up an equation: 2L + 2W = 64, where L is the length of the rock wall and W is the width of the garden. Simplifying the equation, we get L + W = 32. Since the length of the rock wall is equal to the length of the garden, we can rewrite the equation as 2L = 32, which gives us L = 16.
Now we can substitute the value of L back into the equation L + W = 32 to find the width of the garden: 16 + W = 32. Solving for W, we get W = 16. Therefore, the dimensions of the garden that would create the maximum area are 16 meters by 16 meters. The maximum possible area is found by multiplying the length and width of the garden, which is 16 * 16 = 256 square meters.