document.write( "Question 169542: The perimeter of a rectangle window is 32 ft. Find the dimensions of the window that will enclose the largest area. \n" ); document.write( "
Algebra.Com's Answer #125252 by nerdybill(7384)\"\" \"About 
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The perimeter of a rectangle window is 32 ft. Find the dimensions of the window that will enclose the largest area.
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\n" ); document.write( "Let W = width
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\n" ); document.write( "Since perimeter is:
\n" ); document.write( "2(L + W) = 32
\n" ); document.write( "L + W = 16
\n" ); document.write( "L = 16-W
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\n" ); document.write( "Area = W(16-W)
\n" ); document.write( "Area = -W^2 + 16W
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\n" ); document.write( "By inspection, we see (from the -1 coefficient associated with W^2) that it is a parabola which opens downward -- therefore, the \"axis of symmetry\" should give you the max.
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\n" ); document.write( "Axis of symmetry:
\n" ); document.write( "W = -b/2a
\n" ); document.write( "W = -16/2(-1)
\n" ); document.write( "W = 8 feet (width)
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\n" ); document.write( "Length:
\n" ); document.write( "16-W = 16-8 = 8 feet (length)\r
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