document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=750169>Question 750169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 30 cm piece of wire is cut into two pieces. One piece is bent into the shape of a square the other piece is bent into the shape of a rectangle with length to width ratio of 2:1 What are the length's of the two pieces if the sum of the areas of the square and rectangle is a minimum?\r<BR>\n" );
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document.write( "Can you please help me out? Thanks so much in advance:)<BR>\n" );
document.write( "Can you also show the steps it would really help me understand better:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #456465 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=456465\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A 30 cm piece of wire is cut into two pieces.<BR>\n" );
document.write( " One piece is bent into the shape of a square. the other piece is bent into<BR>\n" );
document.write( " the shape of a rectangle with length to width ratio of 2:1<BR>\n" );
document.write( " What are the length's of the two pieces if the sum of the areas of the square<BR>\n" );
document.write( " and rectangle is a minimum?<BR>\n" );
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document.write( "let x = length of the side of square<BR>\n" );
document.write( "let y = length of the width of the rectangle<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2y = Length of rectangle<BR>\n" );
document.write( "So we have<BR>\n" );
document.write( "4x + 2(2y) + 2(y) = 30<BR>\n" );
document.write( "4x + 6y = 30<BR>\n" );
document.write( "6y = 30 - 4x<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "3y = 15 - 2x<BR>\n" );
document.write( "Divide by 3<BR>\n" );
document.write( "y = (5-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x)<BR>\n" );
document.write( "the total area equation<BR>\n" );
document.write( "A = x^2 + (2y*y)<BR>\n" );
document.write( "A = x^2 + 2y^2<BR>\n" );
document.write( "replace y with (5-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x) which is (5-.67x)<BR>\n" );
document.write( "A = x^2 + 2(5-.67x)^2<BR>\n" );
document.write( "FOIL (5-.67x)(5-.67x)<BR>\n" );
document.write( "A = x^2 + 2(25-6.7x+.44x^2)<BR>\n" );
document.write( "A = x^2 + 50 - 13.14x + .88x^2<BR>\n" );
document.write( "A = 1.88x^2 - 13.14x + 50<BR>\n" );
document.write( "Find the minimum by finding the axis of symmetry using x = -b/(2a)<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%28-13.14%29%29%2F%282%2A1.88%29 ALIGN=MIDDLE  ALT=\"%28-%28-13.14%29%29%2F%282%2A1.88%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13.14%2F3.76 ALIGN=MIDDLE  ALT=\"13.14%2F3.76\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 3.5 cm is the side of the square for minimum area, therefore<BR>\n" );
document.write( "4(3.5) = 14 cm is piece made into a square<BR>\n" );
document.write( "Find the piece made into the rectangle<BR>\n" );
document.write( "y = 5 - .67(3.5)<BR>\n" );
document.write( "y = 2.66 cm is the width of the rectangle, therefore<BR>\n" );
document.write( "6(2.66) ~ 16 cm is the piece made into the rectangle<BR>\n" );
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document.write( ":\r<BR>\n" );
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document.write( " </SPAN>\n" );
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