CASE STUDY CHALLENGE
Application of Derivatives: Window Design
A window is in the form of a rectangle surmounted by an equilateral triangle on its length. Let the rectangular part have length and breadth x and y metres respectively.
Based on the given information, answer the following questions :
Answer the following:
| (i) | If the perimeter of the window is 12 m, find the relation between x and y. | [1] |
| (ii) | Using the expression obtained in (i), write an expression for the area of the window as a function of x only. | [1] |
| (iii) | (a) Find the dimensions of the rectangle that will allow maximum light through the window. (use expression obtained in (ii))
— OR —
(b) If it is given that the area of the window is 50 m2, find an expression for its perimeter in terms of x. |
[2] |