document.write( "Question 636491: A farmer has a 150m fencing wire to set up around a rectangular lot beside a river for his ducks and geese. If a 10m opening in the side of the river is left, what would be the length and width for maximum areas? \n" ); document.write( "
Algebra.Com's Answer #401115 by ankor@dixie-net.com(22740)\"\" \"About 
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A farmer has a 150m fencing wire to set up around a rectangular lot beside
\n" ); document.write( " a river for his ducks and geese.
\n" ); document.write( " If a 10m opening in the side of the river is left, what would be the length
\n" ); document.write( " and width for maximum areas?
\n" ); document.write( ":
\n" ); document.write( "Let L = outside length
\n" ); document.write( "then
\n" ); document.write( "(L-10) = river length
\n" ); document.write( "and
\n" ); document.write( "W = the width
\n" ); document.write( ":
\n" ); document.write( "total fence equation
\n" ); document.write( "L + (L-10) + 2W = 150
\n" ); document.write( "2L + 2W = 150 + 10
\n" ); document.write( "2L + 2W = 160
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "L + W = 80
\n" ); document.write( "W = (80-L)
\n" ); document.write( ":
\n" ); document.write( "Area = L * W
\n" ); document.write( "Replace W with (80-L)
\n" ); document.write( "A = L(80-L)
\n" ); document.write( "A = -L^2 + 80L
\n" ); document.write( "A quadratic equation, max area will be the axis of symmetry x=-b/(2a)
\n" ); document.write( "In this equation: a=-1; b=80
\n" ); document.write( "L = \"%28-80%29%2F%282%2A-1%29\"
\n" ); document.write( "L = 40 m, length for max area
\n" ); document.write( "then
\n" ); document.write( "W = 80-40 = 40m width for max area
\n" ); document.write( ":
\n" ); document.write( "40m by 40m for max area (1600 sq/m)\r
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