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Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the area of her patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation. Use the vertex form to find the maximum area.
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\n" ); document.write( "400=2l+2w
\n" ); document.write( "200=l+w
\n" ); document.write( "Area = lw
\n" ); document.write( "l=200-w
\n" ); document.write( "Substitute to get:
\n" ); document.write( "Area = (200-w)w
\n" ); document.write( "Area = 200w-w^2
\n" ); document.write( "This is a quadratec with a=-1, b=200
\n" ); document.write( "Maximum occurs at w=-b/2a = -200/-2 = 100
\n" ); document.write( "Then length = 200-width = 100 ft
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\n" ); document.write( "Using the vertex form on -w^2+200= Area
\n" ); document.write( "w^2-200w = -Area
\n" ); document.write( "Complete the square:
\n" ); document.write( "w^2-200w+100^2 = 100^2-Area
\n" ); document.write( "(w-100)^2 = 10000-Area
\n" ); document.write( "Vertex is (100,10000) meaning the width is 100 ft and
\n" ); document.write( "the Area is 10,000.
\n" ); document.write( "==============
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.\r
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\n" ); document.write( "\n" ); document.write( "Answer:
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