Zara fences off a piece of land next to a wall to make a vegetable garden. [Figure 6.1] The garden is a rectangle with the wall as one side of the rectangle. The area of the garden is 18 square metres. The width of the garden is x metres. (a) The total length of fencing required for the garden is y metres. Show that y = 2x + 18/x.

1. (a)The total length of fencing required for the garden is y metres. Show that y = 2x + 18/x.[1]
2. (b)(i)Complete the table for y = 2x + 18/x. [Table: x values 1, 2, 3, 4, 5, 6, 7, 8, 9. y values missing for x=1, 2, 9, and given for 3, 4, 5, 6, 7, 8 as 12, 12.5, 13.6, 15, 16.6, 18.3 respectively.][2]
3. (b)(ii)On the grid, draw the graph of y = 2x + 18/x for 1 ≤ x ≤ 9. [Figure 6.2][3]
4. (c)Use your graph to find the two possible widths of the garden if 14 metres of fencing is used.[2]
5. (d)(i)The fencing costs $20 per metre. Find the minimum amount it will cost Zara to build the fence.[2]
6. (d)(ii)Zara wants to spend no more than $350 on the fence. Find the greatest possible width of the garden Zara can make.[2]

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