A Window Is In The Form Of A Rectangle Surmounted By A Semi-circle. The Total Area Of Window Is Fixed. What Should Be The Ratio Of The Areas Of The Semi-circular Part And The Rectangular Part So That The Total Perimeter Is Minimum?   

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Question

A window is in the form of a rectangle surmounted by a semi-circle. The total area of window is fixed. What should be the ratio of the areas of the semi-circular part and the rectangular part so that the total perimeter is minimum?   

Solution

Correct option is

None of these

Let A be the total area of the window.   

If 2x be the width of the rectangle and y be the height. 

Let the radius of circle be x.

Perimeter (P) = 2x + 2y + πx   

A is fixed and P is to be minimized.

Eliminating y

                

                 

                 

                 

  

For minimum perimeter,

             

           

 

Testing

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