CASE STUDY CHALLENGE
Optimization: Architectural Design
An architect designs a building for a Company. The design of window on the ground floor is proposed to be different than at the other floors. The window is in the shape of a rectangle whose top length is surmounted by a semi-circular opening. This window has a perimeter of 10 m.
Window Shape
Based on the above information, answer the following :
Answer the following:
| (i) | If 2x and 2y represent the length and breadth of the rectangular portion of the window, then establish a relation between x and y. | [1] |
| (ii) | Find the total area of the window in terms of x. | [1] |
| (iii) | (a) Find the values of x and y for the maximum area of the window.
— OR —
(b) If x and y represent the length and breadth of the rectangle, then establish the expression for the area of the window in terms of x only. |
[2] |