document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=947304>Question 947304</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a rectangle is 22, and its diagonal is \sqrt{61}. Find its dimensions and area, accurate to two decimal places.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #577991 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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/cgi-bin/show-face.mpl?user=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=577991\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let L=length; Let W=Width; Perimeter=P=2(L+W); Diagonal=D=hypotenuse<BR>\n" );
document.write( "L and W are two legs of a right triangle with the diagonal as hypotenuse, so:<BR>\n" );
document.write( "P=2(L+W)<BR>\n" );
document.write( "22=2(L+W) Divide each side by 2<BR>\n" );
document.write( "11=L+W Solve for W, subtract L from each side<BR>\n" );
document.write( "11-L=W<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2BW%5E2=D%5E2 ALIGN=MIDDLE  ALT=\"L%5E2%2BW%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=L%5E2%2BW%5E2=%28sqrt%2861%29%29%5E2 ALIGN=MIDDLE  ALT=\"L%5E2%2BW%5E2=%28sqrt%2861%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2BW%5E2=61 ALIGN=MIDDLE  ALT=\"L%5E2%2BW%5E2=61\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute for W<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2B%2811-L%29%5E2=61 ALIGN=MIDDLE  ALT=\"L%5E2%2B%2811-L%29%5E2=61\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2B%28121-22L%2BL%5E2%29=61 ALIGN=MIDDLE  ALT=\"L%5E2%2B%28121-22L%2BL%5E2%29=61\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L%5E2-22L%2B121=61 ALIGN=MIDDLE  ALT=\"2L%5E2-22L%2B121=61\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 61 from each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L%5E2-22L%2B60=0 ALIGN=MIDDLE  ALT=\"2L%5E2-22L%2B60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=aL%5E2%2BbL%2Bc=0 ALIGN=MIDDLE  ALT=\"aL%5E2%2BbL%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L%5E2%2B-22L%2B60+=+0 ALIGN=MIDDLE  ALT=\"2L%5E2%2B-22L%2B60+=+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=L%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"L%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=%28-22%29%5E2-4%2A2%2A60=4 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-22%29%5E2-4%2A2%2A60=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=4 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--22%2B-sqrt%28+4+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--22%2B-sqrt%28+4+%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=L%5B1%5D+=+%28-%28-22%29%2Bsqrt%28+4+%29%29%2F2%5C2+=+6 ALIGN=MIDDLE  ALT=\"L%5B1%5D+=+%28-%28-22%29%2Bsqrt%28+4+%29%29%2F2%5C2+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5B2%5D+=+%28-%28-22%29-sqrt%28+4+%29%29%2F2%5C2+=+5 ALIGN=MIDDLE  ALT=\"L%5B2%5D+=+%28-%28-22%29-sqrt%28+4+%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=2L%5E2%2B-22L%2B60 ALIGN=MIDDLE  ALT=\"2L%5E2%2B-22L%2B60\"   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=2L%5E2%2B-22L%2B60+=+2%28L-6%29%2A%28L-5%29 ALIGN=MIDDLE  ALT=\"2L%5E2%2B-22L%2B60+=+2%28L-6%29%2A%28L-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6, 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-22%2Ax%2B60+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-22%2Ax%2B60+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "ANSWER:Length is 6 or 5<BR>\n" );
document.write( "If L=6 units, then W=11-L=11-6=5 units<BR>\n" );
document.write( "If L=5 units, then W=11-L=11-5=6 units<BR>\n" );
document.write( "ANSWER: The dimensions are 6 units x 5 units (or 5 units x 6 units)<BR>\n" );
document.write( "The area is the same either way: Area =L x W=6 units x 5 units= 30 square units<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );