document.write( "Question 1117967: A Norman window has the shape of a rectangle surmounted by a semicircle, as shown in the figure below. A Norman window with perimeter 40 ft is to be constructed.Find the dimensions of the rectangular portion of the window, such that the full window admits the greatest amount of light. (Round your answers to two decimal places.) \n" ); document.write( "

Algebra.Com's Answer #733150 by ikleyn(52781) $\"\"$ $\"About$

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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 =   ====>   +  = 40  ====>  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    = 20  ====> x =  =  = 11.20 ft.\r\n" );
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document.write( "Answer.  The maximum area is at x = 11.20 ft.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Be aware: The method on how @josgaritmetic is doing it I S I N C O R R E C T.\r
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