document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=892582>Question 892582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the perimeter of a rectangle is p and its diagnoal is d, the difference between the length and width of the rectangle is ______?\r<BR>\n" );
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document.write( "I have worked several formulas, 2L Plus 2W = p, solved for L, and tryig to solve for W, I have worked it several ways.  I have also used the Pathagoreum theorm, L squared plus w squared = d squared. I have not been able to solve it, begining to wonder if it is a trick problem from instructor. Can you help.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #540607 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39799)</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=540607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This can only be done using variables because no values are given.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2w%2B2L ALIGN=MIDDLE  ALT=\"p=2w%2B2L\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2BL%5E2=d%5E2 ALIGN=MIDDLE  ALT=\"w%5E2%2BL%5E2=d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "You want to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28w-L%29 ALIGN=MIDDLE  ALT=\"abs%28w-L%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "You assume that the constants are d and p.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L=p-2w ALIGN=MIDDLE  ALT=\"2L=p-2w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%28p-2w%29%2F2 ALIGN=MIDDLE  ALT=\"L=%28p-2w%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "substitute into the diagonal equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2B%28p-2w%29%5E2%2F4=d%5E2 ALIGN=MIDDLE  ALT=\"w%5E2%2B%28p-2w%29%5E2%2F4=d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4w%5E2%2B%28p-2w%29%5E2=4d%5E2 ALIGN=MIDDLE  ALT=\"4w%5E2%2B%28p-2w%29%5E2=4d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4w%5E2%2Bp%5E2-4pw%2B4w%5E2-d%5E2=0 ALIGN=MIDDLE  ALT=\"4w%5E2%2Bp%5E2-4pw%2B4w%5E2-d%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8w%5E2-4pw%2Bp%5E2-d%5E2=0 ALIGN=MIDDLE  ALT=\"8w%5E2-4pw%2Bp%5E2-d%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the general solution of  quadratic equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%284p%2B-+sqrt%2816p%5E2-4%2A8%28p%5E2-d%5E2%29%29%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"w=%284p%2B-+sqrt%2816p%5E2-4%2A8%28p%5E2-d%5E2%29%29%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%284p%2B-+sqrt%2816p%5E2-32%28p%5E2-d%5E2%29%29%29%2F16 ALIGN=MIDDLE  ALT=\"w=%284p%2B-+sqrt%2816p%5E2-32%28p%5E2-d%5E2%29%29%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%284p%2B-+4sqrt%28p%5E2-2%28p%5E2-d%5E2%29%29%2F16 ALIGN=MIDDLE  ALT=\"w=%284p%2B-+4sqrt%28p%5E2-2%28p%5E2-d%5E2%29%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28p%2B-+sqrt%28p%5E2-2p%5E2%2B2d%5E2%29%29%2F4 ALIGN=MIDDLE  ALT=\"w=%28p%2B-+sqrt%28p%5E2-2p%5E2%2B2d%5E2%29%29%2F4\"   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%28w=%28p%2B-+sqrt%282d%5E2-p%5E2%29%29%2F4%29 ALIGN=MIDDLE  ALT=\"highlight_green%28w=%28p%2B-+sqrt%282d%5E2-p%5E2%29%29%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----this is just for w.\r<BR>\n" );
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document.write( "What about the other dimension, L?<BR>\n" );
document.write( "... w=(p-2L)/2;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p-2L%29%5E2%2F4%2BL%5E2=d%5E2 ALIGN=MIDDLE  ALT=\"%28p-2L%29%5E2%2F4%2BL%5E2=d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > when substituted into the diagonal equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p-2L%29%5E2%2B4L%5E2=4d%5E2 ALIGN=MIDDLE  ALT=\"%28p-2L%29%5E2%2B4L%5E2=4d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2-4pL%2B4L%5E2%2B4L%5E2=d%5E2 ALIGN=MIDDLE  ALT=\"p%5E2-4pL%2B4L%5E2%2B4L%5E2=d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2-4pL%2B8L%5E2-d%5E2=0 ALIGN=MIDDLE  ALT=\"p%5E2-4pL%2B8L%5E2-d%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8L%5E2-4pL%2Bp%5E2-d%5E2=0 ALIGN=MIDDLE  ALT=\"8L%5E2-4pL%2Bp%5E2-d%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "General Solution,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%284p%2B-+sqrt%2816p%5E2-4%2A8%28p%5E2-d%5E2%29%29%29%2F16 ALIGN=MIDDLE  ALT=\"L=%284p%2B-+sqrt%2816p%5E2-4%2A8%28p%5E2-d%5E2%29%29%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%284p%2B-+sqrt%2816p%5E2-16%2A2%28p%5E2-d%5E2%29%29%29%2F16 ALIGN=MIDDLE  ALT=\"L=%284p%2B-+sqrt%2816p%5E2-16%2A2%28p%5E2-d%5E2%29%29%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%284p%2B-+4sqrt%28p%5E2-2%28p%5E2-d%5E2%29%29%2F16 ALIGN=MIDDLE  ALT=\"L=%284p%2B-+4sqrt%28p%5E2-2%28p%5E2-d%5E2%29%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=%28p%2B-+sqrt%28p%5E2-2p%5E2%2B2d%5E2%29%29%2F4 ALIGN=MIDDLE  ALT=\"L=%28p%2B-+sqrt%28p%5E2-2p%5E2%2B2d%5E2%29%29%2F4\"   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%28L=%28p%2B-+sqrt%282d%5E2-p%5E2%29%29%2F4%29 ALIGN=MIDDLE  ALT=\"highlight_green%28L=%28p%2B-+sqrt%282d%5E2-p%5E2%29%29%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----formula for L.\r<BR>\n" );
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document.write( "<b>YOU can finish this.</b><BR>\n" );
document.write( "Pay attention to both forms for w and L, since each has a PLUS form and a MINUS form.  Remember, you are looking for THE DIFFERENCE or absolute value of w and L.\r<BR>\n" );
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document.write( "Please excuse the lack of rendering in three of the steps.  Tracing the parentheses will be difficult.  The majority of readable steps should be plenty helpful. </SPAN>\n" );
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