document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107112>Question 107112</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780321437266/algebrahomeworkh>Beginning Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The Length of a rectangular label is three times its width. If the length is decreased by 1 while the width stayed the same, the area of the new label would be 44 square centimeters. Find the original length and the width of the label. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #78079 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=78079\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let W=width of label<BR>\n" );
document.write( "Then Length(L)=3W<BR>\n" );
document.write( "Length decreased by  DISABLED_event_one= 3W-1<BR>\n" );
document.write( "Area(A)=L*W<BR>\n" );
document.write( "In this problem, W=W and L=(3W-1), So:\r<BR>\n" );
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document.write( "A=W(3W-1)=44 get rid of parens (distributive law)<BR>\n" );
document.write( "3W^2-W=44 subtract 44 from both sides\r<BR>\n" );
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document.write( "3W^2-W-44=44-44  collect like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3W%5E2-W-44=0 ALIGN=MIDDLE  ALT=\"3W%5E2-W-44=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  quadratic in standard form and it can be factored:<BR>\n" );
document.write( "(Note:  How did I know that it could be factored??? First, I calculated<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28b%5E2-4a%2Ac%29 ALIGN=MIDDLE  ALT=\"sqrt%28b%5E2-4a%2Ac%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >and found it to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28529%29 ALIGN=MIDDLE  ALT=\"sqrt%28529%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23 ALIGN=MIDDLE  ALT=\"23\"   DISABLED_style= \"max-width:90%; height:auto;\" > which tells me that it can probably be factored.  Next, I commenced evaluating the possible factors (a total of eight possibilities) until I found the one that worked.)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283W%2B11%29%28W-4%29=0 ALIGN=MIDDLE  ALT=\"%283W%2B11%29%28W-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3W%2B11=0 ALIGN=MIDDLE  ALT=\"3W%2B11=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3W=-11 ALIGN=MIDDLE  ALT=\"3W=-11\"   DISABLED_style= \"max-width:90%; height:auto;\" >----------------------disregard negative value for width<BR>\n" );
document.write( "and:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w-4=0 ALIGN=MIDDLE  ALT=\"w-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=4 ALIGN=MIDDLE  ALT=\"W=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >cm------------------width<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3W=3%2A4=12 ALIGN=MIDDLE  ALT=\"3W=3%2A4=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm--------------------------original length\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "4*(12-1)=44<BR>\n" );
document.write( "4*11=44<BR>\n" );
document.write( "44=44\r<BR>\n" );
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document.write( "Hope this helps----ptaylor<BR>\n" );
document.write( " </SPAN>\n" );
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