document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=869356>Question 869356</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the perimeter of a rectangle and square are 160 metre each.  the area of rectangle is less than that of square by 100 square metre. find the length of rectangle?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #524143 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=524143\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assign variables.<BR>\n" );
document.write( "s = length of square<BR>\n" );
document.write( "x = rectangle length<BR>\n" );
document.write( "y = rectangle width<BR>\n" );
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document.write( "Find equations and expressions.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4s=160 ALIGN=MIDDLE  ALT=\"4s=160\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2By%29=160 ALIGN=MIDDLE  ALT=\"2%28x%2By%29=160\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Area of square, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2 ALIGN=MIDDLE  ALT=\"s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Area of rectangle, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy ALIGN=MIDDLE  ALT=\"xy\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2-xy=100 ALIGN=MIDDLE  ALT=\"s%5E2-xy=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "SYSTEM OF EQUATIONS:<BR>\n" );
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document.write( "4s=160<BR>\n" );
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document.write( "2x+2y=160<BR>\n" );
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document.write( "s^2-xy=100<BR>\n" );
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document.write( "The question is to find length of the rectangle.  No distinction is necessary about x or y for length; either one is length or width.  First, solve for s and obtain two equations in two unknowns.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=160%2F4 ALIGN=MIDDLE  ALT=\"s=160%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=40 ALIGN=MIDDLE  ALT=\"s=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y=160 ALIGN=MIDDLE  ALT=\"2x%2B2y=160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=80 ALIGN=MIDDLE  ALT=\"x%2By=80\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplified perimeter equation for rectangle.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-xy=100-s%5E2 ALIGN=MIDDLE  ALT=\"-xy=100-s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=s%5E2-100 ALIGN=MIDDLE  ALT=\"xy=s%5E2-100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=40%5E2-100 ALIGN=MIDDLE  ALT=\"xy=40%5E2-100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=1600-100 ALIGN=MIDDLE  ALT=\"xy=1600-100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=1500 ALIGN=MIDDLE  ALT=\"xy=1500\"   DISABLED_style= \"max-width:90%; height:auto;\" > eliminated variable s and simplified area equation.\r<BR>\n" );
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document.write( "SIMPLIFIED SYSTEM:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28xy=1500%29 ALIGN=MIDDLE  ALT=\"highlight_green%28xy=1500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x%2By=80%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x%2By=80%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Solve the simplified system.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=80-x ALIGN=MIDDLE  ALT=\"y=80-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2880-x%29=1500 ALIGN=MIDDLE  ALT=\"x%2880-x%29=1500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80x-x%5E2-1500=0 ALIGN=MIDDLE  ALT=\"80x-x%5E2-1500=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-80x%2B1500=0 ALIGN=MIDDLE  ALT=\"x%5E2-80x%2B1500=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "discriminant, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2880%29%5E2-4%2A1500=6400-6000=400 ALIGN=MIDDLE  ALT=\"%2880%29%5E2-4%2A1500=6400-6000=400\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "General solution for a quadratic equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2880-sqrt%28400%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2880-sqrt%28400%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2880-20%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2880-20%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=30%29 ALIGN=MIDDLE  ALT=\"highlight%28x=30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OR<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2880%2B20%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2880%2B20%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=50%29 ALIGN=MIDDLE  ALT=\"highlight%28x=50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Length of the rectangle can be either 30 OR 50. </SPAN>\n" );
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