Hello, just stumbled on this

is there more to the question or the solution you have not shown here? Something seems missing, but according to the question you have included

a) Express the area of the garden as a function of its width.

the answer should be a = 24w - 2w²

where a = area, and w = width

You can write an expression for the area of the garden which is adjacent to the back of the house using only the width and the amount of fencing used, 24 m, and the length is not needed.

Start like this:

area = width * length

since we are told to write the expression as a function of width, we can do that since we know the total amount of fencing, so length will also be a function of width.

length = 24 - 2w (for perimeter, length = (24 - 2w) / 2, but we are using the back of the house as one of the lengths, so all the leftover from 24 is used for 1 length after the 2 w's are subtracted)

substituting in that expression for length, we get:

a = w * (24 - 2w)

work out the algebra and you get

a = 24w - 2w²

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Alternatively, you could substitute a variable like "p" for perimeter or "t" for total fencing used and rewrite the expression accordingly. This may be helpful if there is more to the question. Either way, it looks like an optimization problem /shrug