document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=283642>Question 283642</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangle is 3cm more than 2 times its width.  If the area of the rectangle is 93cm^2, find the dimensions of the rectangle.  Enter your answers in the blanks.  Enter only the numeric values rounded to the nearest thousandth of centimeter   Width=________cm, Length=_____________cm. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #205843 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=205843\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> L = length<BR>\n" );
document.write( "W = width<BR>\n" );
document.write( "A = area<BR>\n" );
document.write( "A = L*W<BR>\n" );
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document.write( "L = 2W + 3 <BR>\n" );
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document.write( "A = 93 cm^2<BR>\n" );
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document.write( "Substitute L = 2W+3 in the area equation to solve.<BR>\n" );
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document.write( "L*W = 93 cm^2<BR>\n" );
document.write( "(2W +3) * W = 93<BR>\n" );
document.write( "2W^2 + 3W = 93<BR>\n" );
document.write( "2W^2 + 3W -93 = 0<BR>\n" );
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document.write( "This does not factor nicely, so you need to use the quadratic equation.<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=aW%5E2%2BbW%2Bc=0 ALIGN=MIDDLE  ALT=\"aW%5E2%2BbW%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%5E2%2B3W%2B-93+=+0 ALIGN=MIDDLE  ALT=\"2W%5E2%2B3W%2B-93+=+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=W%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"W%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=%283%29%5E2-4%2A2%2A-93=753 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283%29%5E2-4%2A2%2A-93=753\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=753 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+=+%28-3%2B-sqrt%28+753+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-3%2B-sqrt%28+753+%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=W%5B1%5D+=+%28-%283%29%2Bsqrt%28+753+%29%29%2F2%5C2+=+6.11021136700612 ALIGN=MIDDLE  ALT=\"W%5B1%5D+=+%28-%283%29%2Bsqrt%28+753+%29%29%2F2%5C2+=+6.11021136700612\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5B2%5D+=+%28-%283%29-sqrt%28+753+%29%29%2F2%5C2+=+-7.61021136700612 ALIGN=MIDDLE  ALT=\"W%5B2%5D+=+%28-%283%29-sqrt%28+753+%29%29%2F2%5C2+=+-7.61021136700612\"   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=2W%5E2%2B3W%2B-93 ALIGN=MIDDLE  ALT=\"2W%5E2%2B3W%2B-93\"   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=2W%5E2%2B3W%2B-93+=+2%28W-6.11021136700612%29%2A%28W--7.61021136700612%29 ALIGN=MIDDLE  ALT=\"2W%5E2%2B3W%2B-93+=+2%28W-6.11021136700612%29%2A%28W--7.61021136700612%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6.11021136700612, -7.61021136700612.\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%2B3%2Ax%2B-93+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3%2Ax%2B-93+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "This provides two solutions:  W=6.11 and W=-7.61.<BR>\n" );
document.write( "W cannot be negative, so the approximate value is W=6.11.<BR>\n" );
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document.write( "Substituting, W=6.11, we can find L.<BR>\n" );
document.write( "L = 93/6.11<BR>\n" );
document.write( "L = 15.22 cm<BR>\n" );
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document.write( "Checking, does the area = 93 cm^2?<BR>\n" );
document.write( "(15.22)(6.11) = 92.9942 cm^2, which is close enough to 93.<BR>\n" );
document.write( "Correct.<BR>\n" );
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document.write( "Checking, does L = 2W + 3?<BR>\n" );
document.write( "2W = 2*6.11 = 12.22 cm<BR>\n" );
document.write( "12.22 + 3 = 15.22 cm<BR>\n" );
document.write( "Correct.<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "L = 15.22 cm<BR>\n" );
document.write( "W = 6.11 cm<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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