document.write( "Question 203861: A rectangular garden is to be fenced with 100 meters of fencing. The wall of the house will be one side of the garden, so the fencing is needed only on three sides. What is the largest garden possible? \n" ); document.write( "
Algebra.Com's Answer #153803 by nerdybill(7384)\"\" \"About 
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A rectangular garden is to be fenced with 100 meters of fencing. The wall of the house will be one side of the garden, so the fencing is needed only on three sides. What is the largest garden possible?
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\n" ); document.write( "Let x = width
\n" ); document.write( "and y = length
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\n" ); document.write( "Perimeter:
\n" ); document.write( "2x+y = 100
\n" ); document.write( "Solving for y:
\n" ); document.write( "y = 100-2x
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\n" ); document.write( "Area = xy
\n" ); document.write( "Area = x(100-2x)
\n" ); document.write( "Area = 100x-2x^2
\n" ); document.write( "Area = -2x^2+100x
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\n" ); document.write( "This is a parabola that opens downward -- therefore, finding the vertex gives you the maximum.
\n" ); document.write( "axis of symmetry = -b/(2a) = -100/(-4) = 25
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\n" ); document.write( "Largest possible area then is:
\n" ); document.write( "Area = -2x^2+100x
\n" ); document.write( "Area = -2(25)^2+100(25)
\n" ); document.write( "Area = -1250+2500
\n" ); document.write( "Area = 1250 square meters\r
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