3. (a) This is a question on the largest rectangle that can be inscribed in a semicircle of radius r as shown in Fig. 4. -T 2x y Area A Figure 4 (i) Show that the area of the rectangle A is given by A = 2√√₁²-² 2 I + y = r (x,y) Page 9 20 (ii) Determine the dimensions r and y in terms of the radius r so that we have maximum area. →x

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