 Hello and welcome to the session, let us understand the following question which says, a window is in the form of a rectangle surmounted by a semicircular opening. The total parameter of the window is 10 meter. Find the dimension of the window to admit maximum light through the whole opening. Now let's proceed on to the solution. But before that, let us see the figure for the question. Here we have ABCD as a rectangular window which is surmounted by a semicircular opening. Let X be the radius of the semicircular opening. Then 2H will be the length of the rectangle and let 2Y will be the width of the rectangle. Then parameter will be equal to the total length of the window that is 2X. The length of this semicircular opening will be half the area of circle that is half multiplied by 2 pi X plus 2Y. This 2 and 2 gets cancelled so it is equal to 2X i is equal to 4Y. Now given to us, the total parameter of the window is find the dimension of the window to admit. It will be admitted when the area of the figure is maximum. So here, of this rectangular part, the circle that is