question_answer 1)

A window is in the form of a rectangle surmounted be semi-circular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.

Answer:

Let x be the radius of the semicircle        of rectangle = 2x       Let width of rectangle is y       Give total perimeter of the window = 10 m                                            ? (1)       Combined area of the rectangle and semi circle       = Area of the window                             (Using (1))                                                  Now             A is maximum when             (1)