SOLUTION: A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimensions of the rectangular part of a Norman window to

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Question 1157160: A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimensions of the rectangular part of a Norman window to allow in as much light as possible, if there are only 12 ft of the frame material available?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
x, the diameter and dimension of the one side with the semicircle
w, the other rectangular dimension

Area A:



Amount of frame material, 12 feet:



The two equations are just after starting, and not the finished solution ,...
Answer by ikleyn(52896)   (Show Source): You can put this solution on YOUR website!
.

Let x = width and diameter;

    y = height of the rectangle part.


Then the perimeter   

P =   ====>   +  = 12  ====>  y = .


The area A =  +  =  +  =  -  -  +  =  +  - 



Then  the condition for the maximum area   = 0  takes the form


 = 0,   or    = 6  ====> x =  =  = 3.36 ft.


Answer.  The maximum area is at x = 3.36 ft  (the width), 

         y =  =  = 1.68 ft (the height).

Solved.


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