b. Question 5b is worth 20 marks A window frame is shown in Figure 1 below. The thickness of the frame and the struts within the frame are small compared to the other dimensions. and do not need to be accounted for separately. \\' || Figure 1 Awindow frame made up ofeight equal rectangles. Not drawn to scale. Show description v i. If 18 metres of frame are used to go around the outside perimeter of the window. show that: y = (94h)! 2 Explain each step of your working. [4 marks) ii. Show that the area of the window, A. can be expressed in terms of h by the quadratic equation: A = 36h 16h2 Explain each step of your working. (4 marks) iii. Using the method described in Section 11.3 of the Part 3 book. find the overall dimensions of the frame (the height and width of the window) that make the area of the window a maximum. Explain each step of your working. [4 marks) iv. Using a spreadsheet. plot a graph showing the area of the window. A, as a function of h. Paste a copy of the graph into your TMA. (6 marks) v. Using the height and width of the window you found in Part 3 above. calculate the maximum area of the window. Compare this with the value shown in the graph you produced in Part 4 of this Question. [2 marks)