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

Explanation

Let the length of the window be `x m` and breadth of the window be `y m`.

Its total perimeter `=10 m`

`implies 2y+x+x/2pi=10implies y={20-x(2+pi)}/4`

Area of the window `=xy+1/2pi{x^2}/4`

`implies A=1/8(40x-x^2(pi+4))`

`{dA}/{dx}=-40-2x(pi+4)`

Put `{dA}/{dx}=0`

Thus `40-2x(pi+4)=0 `

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