document.write( "Question 798439: A 40-inch length of wire is cut in two. One of the pieces is bent to form a square and the other is bent to form a rectangle three times as long as wide. If the combined area of the square and the rectangle is 55 3/4 inches, where was the wire cut? There are two places where the wire can be cut. One of them is a fraction answer. \n" ); document.write( "
Algebra.Com's Answer #482209 by ankor@dixie-net.com(22740)\"\" \"About 
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A 40-inch length of wire is cut in two.
\n" ); document.write( " One of the pieces is bent to form a square and the other is bent to form a rectangle three times as long as wide.
\n" ); document.write( " If the combined area of the square and the rectangle is 55 3/4 inches, where was the wire cut?
\n" ); document.write( " There are two places where the wire can be cut.
\n" ); document.write( " One of them is a fraction answer.
\n" ); document.write( ":
\n" ); document.write( "Let x = length of the one side of the square
\n" ); document.write( "then
\n" ); document.write( "x^2 = the area of the square
\n" ); document.write( "and
\n" ); document.write( "(40-4x) = the perimeter of the rectangle
\n" ); document.write( "Let W = the width of the rectangle
\n" ); document.write( "then
\n" ); document.write( "3W = the length of the rectangle
\n" ); document.write( "therefore
\n" ); document.write( "2(3W) + 2W = 40 - 4x
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "3W + W = 20 - 2x
\n" ); document.write( "4W = 20-2x
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "2W = 10 - x
\n" ); document.write( "x = -2W + 10
\n" ); document.write( ":
\n" ); document.write( "\"the combined area of the square and the rectangle is 55 3/4 inches\"
\n" ); document.write( "x^2 + 3W^2 = 55.75
\n" ); document.write( "Replace x with (-2W+10)
\n" ); document.write( "(-2w+10)^2 + 3W^2 = 55.75
\n" ); document.write( "Foil
\n" ); document.write( "4w^2 -40w + 100 + 3w^2 = 55.75
\n" ); document.write( "7W^2 - 40w + 100 - 55.75 = 0
\n" ); document.write( "7w^2 - 40w + 44.25 = 0
\n" ); document.write( "Using the quadratic formula, two solutions
\n" ); document.write( "w = 1.5, we will use this one
\n" ); document.write( "w = 4.2143
\n" ); document.write( "find x
\n" ); document.write( " x = -2(1.5) + 10
\n" ); document.write( " x = 7 in, the side of square
\n" ); document.write( "then
\n" ); document.write( "4(7) = 28 inches cut the wire
\n" ); document.write( ":
\n" ); document.write( "Check this, 40 - 28 = 12 in is perimeter of the rectangle
\n" ); document.write( "see if this checks out: w= 1.5, L = 4.5
\n" ); document.write( "2(4.5) + 2(1.5) = 12\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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