Question

A window is in the form of rectangle surmounted by a semicircular 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 1

Let x and y be the length and breadth of the rectangular window.
Radius of the semicircular opening =x/2

It is given that the perimeter of the window is 10 m.

Therefore, by second derivative test, the area is the maximum when length . x= 20/(π+4) m.
Now,

Hence, the required dimensions of the window to admit maximum light is given