Adil wants to fence off some land as an enclosure for his chickens. The enclosure will be a rectangle with an area of 50 m². [Diagram: Rectangle with 50 m² area and side x]

1. (a)The enclosure is x m long. Show that the total length of fencing, Lm, required for the enclosure is given by L = 2x + 100/x.[2]
2. (b)The table below shows some values of x and the corresponding values of L, correct to one decimal place where appropriate, for L = 2x + 100/x. Complete the table. x | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 L | 54 | 33 | 28.7 | 28.5 | 30 | 32.3 | 35.1 | 38.3 | |[2]
3. (c)On the grid opposite draw a horizontal x-axis for 0 ≤ x ≤ 20 using a scale of 1 cm to represent 2 m and a vertical L-axis for 0 < L ≤ 60 using a scale of 2 cm to represent 10m. On the grid, plot the points given in the table and join them with a smooth curve.[3]
4. (d)Adil only has 40m of fencing. Use your graph to find the range of values of x that he can choose.[2]
5. (e)(i)Find the minimum length of fencing Adil could use for the enclosure.[1]
6. (e)(ii)Find the length and width of the enclosure using this minimum length of fencing. Give your answers correct to the nearest metre.[1]
7. (f)Suggest a suitable length and width for an enclosure of area 100m², that uses the minimum possible length of fencing.[1]

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