Answer Happy

Question 11 (15 marks) The diagram at right shows a proposal to construct two adjoining enclosures to keep pigs, a rectangular one attached to a triangular one. All measurements are in metres and the layout of the site is such that the approximate total area of the enclosures cannot be more than 184m². (a) Clearly show that, if an enclosure of largest area is built, then 12x² +8xy = 184. (b) The total length of fencing required. (in metres), is given by L=26x + 2y. (1) Use the result in (a) to show that L can be written as L=23x++ metres. 46 15 [4 marks] [2 marks]

(ii) Hence find the values of x and y which will ensure that the total length of fencing is minimum. [6 marks] (iii) When you buy the fencing it must be bought in multiples of 5 metre lengths. Find the minimum cost of the fencing if one 5 metre length costs $184.50. [3 marks]