document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #779976 by ikleyn(52906) $\"\"$ $\"About$

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document.write( "Let x = width and diameter;\r\n" );
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document.write( "    y = height of the rectangle part.\r\n" );
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document.write( "Then the perimeter   \r\n" );
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document.write( "P =   ====>   +  = 12  ====>  y = .\r\n" );
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document.write( "The area A =  +  =  +  =  -  -  +  =  +  - \r\n" );
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document.write( "Then  the condition for the maximum area   = 0  takes the form\r\n" );
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document.write( " = 0,   or    = 6  ====> x =  =  = 3.36 ft.\r\n" );
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document.write( "Answer.  The maximum area is at x = 3.36 ft  (the width), \r\n" );
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document.write( "         y =  =  = 1.68 ft (the height).\r\n" );
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