document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=930748>Question 930748</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle is drawn so the width is 2 inches longer than the height. If the rectangle's diagonal measurement is 58 inches, find the height.\r<BR>\n" );
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document.write( "Give your answer rounded to 1 decimal place. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #565259 by </B><A HREF=/tutors/aboutme.mpl?userid=rcdodds><B>rcdodds(6)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rcdodds><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=rcdodds><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=565259\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well let's set this up as a system of equations.\r<BR>\n" );
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document.write( "Allow \"w\" to be the width.<BR>\n" );
document.write( "Allow \"h\" to be the height.<BR>\n" );
document.write( "Allow \"d\" to be the diagonal.\r<BR>\n" );
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document.write( "We know from the Pythagorean Theorem that...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "but in this case<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=w ALIGN=MIDDLE  ALT=\"a=w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=h ALIGN=MIDDLE  ALT=\"b=h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=d=58 ALIGN=MIDDLE  ALT=\"c=d=58\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we can say that...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+%2B+h%5E2+=+d%5E2+=+58%5E2 ALIGN=MIDDLE  ALT=\"w%5E2+%2B+h%5E2+=+d%5E2+=+58%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Which is our first equation.<BR>\n" );
document.write( "Our second equation comes from the \"width is 2 inches longer than the height\", which means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+h+%2B+2 ALIGN=MIDDLE  ALT=\"w+=+h+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Substituting that into the first equation we can solve using algebra to find the height.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+%2B+h%5E2+=+58%5E2 ALIGN=MIDDLE  ALT=\"w%5E2+%2B+h%5E2+=+58%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28h+%2B+2%29%5E2+%2B+h%5E2+=+58%5E2 ALIGN=MIDDLE  ALT=\"%28h+%2B+2%29%5E2+%2B+h%5E2+=+58%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+%2B+4h+%2B+4+%2B+h%5E2+=+58%5E2 ALIGN=MIDDLE  ALT=\"h%5E2+%2B+4h+%2B+4+%2B+h%5E2+=+58%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2h%5E2+%2B+4h+%2B+4+=+58%5E2 ALIGN=MIDDLE  ALT=\"2h%5E2+%2B+4h+%2B+4+=+58%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2h%5E2+%2B+4h+-+3360+=+0 ALIGN=MIDDLE  ALT=\"2h%5E2+%2B+4h+-+3360+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+%2B+2h+-+1680+=+0 ALIGN=MIDDLE  ALT=\"h%5E2+%2B+2h+-+1680+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\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=ah%5E2%2Bbh%2Bc=0 ALIGN=MIDDLE  ALT=\"ah%5E2%2Bbh%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1h%5E2%2B2h%2B-1680+=+0 ALIGN=MIDDLE  ALT=\"1h%5E2%2B2h%2B-1680+=+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=h%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"h%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=%282%29%5E2-4%2A1%2A-1680=6724 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%282%29%5E2-4%2A1%2A-1680=6724\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=6724 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+=+%28-2%2B-sqrt%28+6724+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-2%2B-sqrt%28+6724+%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=h%5B1%5D+=+%28-%282%29%2Bsqrt%28+6724+%29%29%2F2%5C1+=+40 ALIGN=MIDDLE  ALT=\"h%5B1%5D+=+%28-%282%29%2Bsqrt%28+6724+%29%29%2F2%5C1+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B2%5D+=+%28-%282%29-sqrt%28+6724+%29%29%2F2%5C1+=+-42 ALIGN=MIDDLE  ALT=\"h%5B2%5D+=+%28-%282%29-sqrt%28+6724+%29%29%2F2%5C1+=+-42\"   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=1h%5E2%2B2h%2B-1680 ALIGN=MIDDLE  ALT=\"1h%5E2%2B2h%2B-1680\"   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=1h%5E2%2B2h%2B-1680+=+1%28h-40%29%2A%28h--42%29 ALIGN=MIDDLE  ALT=\"1h%5E2%2B2h%2B-1680+=+1%28h-40%29%2A%28h--42%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 40, -42.\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+1%2Ax%5E2%2B2%2Ax%2B-1680+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-1680+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Rounding this to one decimal place, we get our final answer to be 40 inches.<BR>\n" );
document.write( "Note that we ignore the negative result from the quadratic formula because you can't have a negative distance. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );