document.write( "Question 50358: an teacher wants to use 19 feet of scalloped border to block off a rectangular region on her bulletiin board. What is the max area that she can enclose with the border? \n" ); document.write( "

Algebra.Com's Answer #33461 by stanbon(75887) $\"\"$ $\"About$

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an teacher wants to use 19 feet of scalloped border to block off a rectangular region on her bulletiin board. What is the max area that she can enclose with the border?
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\n" ); document.write( "The perimeter must be 19 feet, so:
\n" ); document.write( "P=2*length + 2*width = 19
\n" ); document.write( "length + width = 9.5
\n" ); document.write( "length = 9.5-width
\n" ); document.write( "------
\n" ); document.write( "Area = (length)(width)
\n" ); document.write( "Area = (9.5-w)(w)
\n" ); document.write( "Area = 9.5w-w^2
\n" ); document.write( "--------
\n" ); document.write( "This is a quadratic with a=-1,b=9.5
\n" ); document.write( "The maximum point is at w=-b/2a= 9.5/2= 4.75
\n" ); document.write( "So width is 4.75 ft.
\n" ); document.write( "length = 9.5-4.75 = 4.75 ft.
\n" ); document.write( "The teacher will get the maximum area if she lets the rectangle
\n" ); document.write( "be a square with a side of 5.75 ft.\r
\n" ); document.write( "\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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