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Answer :

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



=0




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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