document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206251>Question 206251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Wondering if I am on the right track.  I need to determine a quadratic equation to solve the problem and also solve the problem.  My word question is as follows:   The perimeter of a rectangle is 34 cm and the diagonal is 13 cm.  Determine the lengths of the side of the rectangle.\r<BR>\n" );
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document.write( "I am setting up my equation as follows:<BR>\n" );
document.write( "    2x + 2y = 34<BR>\n" );
document.write( "    x^2 + y^2 = 169\r<BR>\n" );
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document.write( "I then determine (x) by the following equation:<BR>\n" );
document.write( "    2x + 2y = 34<BR>\n" );
document.write( "    2x = 34 - 2y<BR>\n" );
document.write( "    x = 17 - y\r<BR>\n" );
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document.write( "Then I am taking the following equation to come up with a quadratic equation:<BR>\n" );
document.write( "    (17-y)^2 + y^2 = 169<BR>\n" );
document.write( "    189 - 34y + y^2 + y^2 = 169<BR>\n" );
document.write( "    2y^2 - 34y = -20<BR>\n" );
document.write( "    2y^2 - 34y + 20 = 0\r<BR>\n" );
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document.write( "Then my final answer (?) after calculating the quadratic equation is:\r<BR>\n" );
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document.write( "    x = 34 + or - 498 / 4  <BR>\n" );
document.write( "    x = 133 and x = 116\r<BR>\n" );
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document.write( "My question is, am I doing this correctly or am I missing a step?\r<BR>\n" );
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document.write( "Your input would be greatly appreciated.\r<BR>\n" );
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document.write( "Lori </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #155812 by </B><A HREF=/tutors/aboutme.mpl?userid=Targetweek><B>Targetweek(62)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Targetweek><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=155812\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Yes you are doing it correctly but you messed up when you tried to solve the quadratic equation because...<BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17-y%29%5E2+%2B+y%5E2+=+169 ALIGN=MIDDLE  ALT=\"17-y%29%5E2+%2B+y%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28289%29+-+34y+%2B+y%5E2+%2B+y%5E2+=+169 ALIGN=MIDDLE  ALT=\"highlight%28289%29+-+34y+%2B+y%5E2+%2B+y%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%5E2+=+289 ALIGN=MIDDLE  ALT=\"17%5E2+=+289\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%5E2+%3C%3E+189 ALIGN=MIDDLE  ALT=\"17%5E2+%3C%3E+189\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So besides that you did it right but i'll go ahead and finish it for you<BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=289+-+34y+%2B+2y%5E2+=+169 ALIGN=MIDDLE  ALT=\"289+-+34y+%2B+2y%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%5E2+-+34y+%2B+289+-+169+=+169-169 ALIGN=MIDDLE  ALT=\"2y%5E2+-+34y+%2B+289+-+169+=+169-169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%5E2+-+34y+%2B+120+=+0 ALIGN=MIDDLE  ALT=\"2y%5E2+-+34y+%2B+120+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B-34x%2B120+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-34x%2B120+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-34%29%5E2-4%2A2%2A120=196 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-34%29%5E2-4%2A2%2A120=196\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=196 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--34%2B-sqrt%28+196+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--34%2B-sqrt%28+196+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-34%29%2Bsqrt%28+196+%29%29%2F2%5C2+=+12 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-34%29%2Bsqrt%28+196+%29%29%2F2%5C2+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-34%29-sqrt%28+196+%29%29%2F2%5C2+=+5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-34%29-sqrt%28+196+%29%29%2F2%5C2+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B-34x%2B120 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-34x%2B120\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B-34x%2B120+=+2%28x-12%29%2A%28x-5%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-34x%2B120+=+2%28x-12%29%2A%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 12, 5.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-34%2Ax%2B120+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-34%2Ax%2B120+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Since your solutions for x are 12 and 5, the side lengths are 12 and 5 because you get the same answer if x=12,y=5 as x=5,y=12<BR>\n" );
document.write( "hope that helped!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );