document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=862076>Question 862076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am helping my daughter do her homework and we are stuck on this, please help me explain it to her.\r<BR>\n" );
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document.write( "The length of a rectangle is 1cm less than four times its width.  If the area of the rectangle is 39cm (squared), what  is the width and the length of the rectangle.\r<BR>\n" );
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document.write( "Many thanks, </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #519437 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=519437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> w for width<BR>\n" );
document.write( "L for length<BR>\n" );
document.write( "k = how much is length than the width; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3E0 ALIGN=MIDDLE  ALT=\"k%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "m = a factor applied to the width as part of description.  Usually this is a natural number.<BR>\n" );
document.write( "A = area of rectangegle<BR>\n" );
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document.write( "The only unknown variables are L and w.<BR>\n" );
document.write( "You are given that k=1, m=4, A=39.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=-k%2Bm%2Aw ALIGN=MIDDLE  ALT=\"L=-k%2Bm%2Aw\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the first sentence in the description.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=wL=A ALIGN=MIDDLE  ALT=\"wL=A\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the second sentence in description.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%28-k%2Bmw%29=A ALIGN=MIDDLE  ALT=\"w%28-k%2Bmw%29=A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%28mw-k%29=A ALIGN=MIDDLE  ALT=\"w%28mw-k%29=A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mw%5E2-kw=A ALIGN=MIDDLE  ALT=\"mw%5E2-kw=A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mw%5E2-kw-A=0 ALIGN=MIDDLE  ALT=\"mw%5E2-kw-A=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Values given may often be chosen to make the resulting quadratic equation to be factorable.  This will make the solution for w easily found.  In \"Introductory Algebra\", you can usually depend on this factorability; after that, you cannot always depend on this factorability and will need to use general solution of a quadratic equation.  Is this example factorable?\r<BR>\n" );
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document.write( "If not, or even if it is, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28k%2Bsqrt%281-4%2Am%28-A%29%29%29%2F%282m%29 ALIGN=MIDDLE  ALT=\"w=%28k%2Bsqrt%281-4%2Am%28-A%29%29%29%2F%282m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=%28k%2Bsqrt%281%2B4mA%29%29%2F%282m%29%29 ALIGN=MIDDLE  ALT=\"highlight%28w=%28k%2Bsqrt%281%2B4mA%29%29%2F%282m%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, choosing the form with the positive square root, because we know w must be positive.<BR>\n" );
document.write( " </SPAN>\n" );
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