10 Adil wants to fence off some land as an enclosure for his chickens. The enclosure will be a rectangle with an area of 50 m^2. (a) The enclosure is x m long. Show that the total length of fencing, L m, required for the enclosure is given by L=2x+ 100/x (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. (c) On the grid opposite draw a horizontal x-axis for 0 =< x =< 20 using a scale of 1 cm to represent 2m and a vertical L-axis for 0 =< L =< 60 using a scale of 2 cm to represent 10 m. On the grid, plot the points given in the table and join them with a smooth curve. (d) Adil only has 40 m of fencing. Use your graph to find the range of values of x that he can choose. (e) (i) Find the minimum length of fencing Adil could use for the enclosure. (ii) Find the length and width of the enclosure using this minimum length of fencing. Give your answers correct to the nearest metre. (f) Suggest a suitable length and width for an enclosure of area 100 m^2, that uses the minimum possible length of fencing.