document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=442589>Question 442589</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, \r<BR>\n" );
document.write( "\n" );
document.write( "I was wondering if you would be able to help me out on this problem. I'm not sure where to start:\r<BR>\n" );
document.write( "\n" );
document.write( "The area of the parallelogram is 108 square miles. Find it's base & height. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305297 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305297\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> As you know, the area of a parallelogram = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Ah ALIGN=MIDDLE  ALT=\"b%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" >. It seems as though we need more information to do this.  Please update your question so that I am able to help you further.<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "It seems as though from your description that the base is (2x+6) as well as the height.\r<BR>\n" );
document.write( "\n" );
document.write( "Knowing this, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B6%29%2A%282x%2B6%29+=+4x%5E2+%2B+24x+%2B+36+=+108 ALIGN=MIDDLE  ALT=\"%282x%2B6%29%2A%282x%2B6%29+=+4x%5E2+%2B+24x+%2B+36+=+108\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Then, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B24x+-72+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B24x+-72+=+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=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=4x%5E2%2B24x%2B-72+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B24x%2B-72+=+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=%2824%29%5E2-4%2A4%2A-72=1728 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2824%29%5E2-4%2A4%2A-72=1728\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1728 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+=+%28-24%2B-sqrt%28+1728+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-24%2B-sqrt%28+1728+%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-%2824%29%2Bsqrt%28+1728+%29%29%2F2%5C4+=+2.19615242270663 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2824%29%2Bsqrt%28+1728+%29%29%2F2%5C4+=+2.19615242270663\"   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-%2824%29-sqrt%28+1728+%29%29%2F2%5C4+=+-8.19615242270663 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2824%29-sqrt%28+1728+%29%29%2F2%5C4+=+-8.19615242270663\"   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=4x%5E2%2B24x%2B-72 ALIGN=MIDDLE  ALT=\"4x%5E2%2B24x%2B-72\"   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=4x%5E2%2B24x%2B-72+=+4%28x-2.19615242270663%29%2A%28x--8.19615242270663%29 ALIGN=MIDDLE  ALT=\"4x%5E2%2B24x%2B-72+=+4%28x-2.19615242270663%29%2A%28x--8.19615242270663%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2.19615242270663, -8.19615242270663.\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+4%2Ax%5E2%2B24%2Ax%2B-72+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B24%2Ax%2B-72+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++2.1962 ALIGN=MIDDLE  ALT=\"x+=++2.1962\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "So 2*2.1962 + 6 = 10.393\r<BR>\n" );
document.write( "\n" );
document.write( "So the base and height is 10.393 miles.\r<BR>\n" );
document.write( "\n" );
document.write( "To check, 10.393 * 10.393 = 108.01 miles.\r<BR>\n" );
document.write( "\n" );
document.write( "Close enough. Haha.\r<BR>\n" );
document.write( "\n" );
document.write( "Let me know if you figure out if the height or base is something other than (2x+6).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );