document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935055>Question 935055</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangle is 7yds<BR>\n" );
document.write( "less than three times the width, and the area of the rectangle is 66yds^2<BR>\n" );
document.write( " . Find the dimensions of the rectangle.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568169 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=568169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> L for length, w for width.<BR>\n" );
document.write( "A for area.<BR>\n" );
document.write( "L and w are unknown.\r<BR>\n" );
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document.write( "The length of a rectangle is k yards<BR>\n" );
document.write( "less than m times the width w, and the area of the rectangle is A yds^2.<BR>\n" );
document.write( "Find the dimensions, w and L.\r<BR>\n" );
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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;\" >,    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=mw-k ALIGN=MIDDLE  ALT=\"L=mw-k\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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=highlight_green%28mw%5E2-kw-A=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%28mw%5E2-kw-A=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Beginners would rely on the quadratic expression being factorable when m, k, and A are substituted,<BR>\n" );
document.write( "and then solution for w would be found that way (factoring).  Intermediate level and higher students<BR>\n" );
document.write( "could solve for w either by quadratic formula solution, or competing the square.\r<BR>\n" );
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document.write( "Directly using general solution,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=%28k%2B-+sqrt%28k%5E2-4%2Am%2AA%29%29%2F%282m%29%29 ALIGN=MIDDLE  ALT=\"highlight%28w=%28k%2B-+sqrt%28k%5E2-4%2Am%2AA%29%29%2F%282m%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "One of those will make sense but not the other.  Substitute the values for k, m, and A, evaluate w,<BR>\n" );
document.write( "and then use the value to evaluate L.\r<BR>\n" );
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