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The diagram shows the dimensions in metres of an L-shaped garden. The perimeter of the garden is 48 m .
- Find an expression for \(y\) in terms of \(x\).
- Given that the area of the garden is \(A \mathrm {~m} ^ { 2 }\), show that \(A = 48 x - 8 x ^ { 2 }\).
- Given that \(x\) can vary, find the maximum area of the garden, showing that this is a maximum value rather than a minimum value.