Let x and y be the length and breadth of the rectangular window.
Radius of the semi - circular opening =
It is given that the perimeter of the window is 10m.
⇒ x + 2y +
Therefore, Area of the window (A) is given by
Now, , then
Then, when x = then < 0.
Therefore, by second derivative test, the area is maximum when length
x = m.
Now, y =
Therefore, the required dimensions of the window to admit maximum light is given by length = m and breadth =m.
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