document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=66492>Question 66492</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me answer this question.\r<BR>\n" );
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document.write( "A wire 36 m long is cut into two pieces. Each piece is bent to form a rectangle which is 1.0 m longer than it is wide. How long should each piece to be minimize the sum of the areas of the two rectangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #47199 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=47199\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A wire 36 m long is cut into two pieces. Each piece is bent to form a rectangle which is 1.0 m longer than it is wide. How long should each piece to be minimize the sum of the areas of the two rectangle?<BR>\n" );
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document.write( "Let the two pieces be x and 36-x<BR>\n" );
document.write( "Using the \"x\" piece to form a proper rectangle get sides of (x-1)/2 and (x+1)/2<BR>\n" );
document.write( "This rectangle has Area=(x^2-1)/4<BR>\n" );
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document.write( "Using the \"36-x\" piece to for a proper rectangle get sides of<BR>\n" );
document.write( "(35-x)/2 and (37-x)/2<BR>\n" );
document.write( "This rectangle has Area=(x^2-72x+(35)(37))/4<BR>\n" );
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document.write( "Adding the two area you get (1/4)(2x^2-72x+C), C is a constant<BR>\n" );
document.write( "Taking the derivative you get Area'=(1/4)(4x-72)=x-18<BR>\n" );
document.write( "Checking for minumum you get x-18=0 or x=18 meters<BR>\n" );
document.write( "Each piece should be 18 meters.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
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