Let’s break down the problem and solve step-by-step based on the details provided:

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i) Relation for Total Length of Fencing Wire and Expression for A(x):

Let:

• $x$: Length of the side of the garden perpendicular to the brick wall (in meters).
• $y$: Length of the side of the garden parallel to the brick wall (in meters).

Assume:

• Only three sides of the garden are fenced, as one side is adjacent to the brick wall.

Total Length of Fencing Wire:

The fencing wire is used along the two $x$-sides (perpendicular to the brick wall) and the $y$-side (parallel to the brick wall). Thus: $\text{Total length of fencing wire} = 2x + y.$

Let the total length of the fencing wire be denoted as $L$. Hence: $L = 2x + y.$

Rearranging to express $y$ in terms of $L$ and $x$: $y = L - 2x.$

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Area of the Garden, $A(x)$:

The area $A(x)$ of the rectangular garden is: $A(x) = x \cdot y.$