document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=542362>Question 542362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the length of one rectangular field is 400 meters more than the side of a square field. The width of the rectangular field is 100 meters more than the side of the square field. If the rectangular field has twice the area of the square field, what are the dimensions of each field?\r<BR>\n" );
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document.write( "I came up with 2A^2=(A+400)(A+100)<BR>\n" );
document.write( "A being equal to the side of the square, 2A^2 being equal to the squares area<BR>\n" );
document.write( "I'm not sure where to go from there because when I foiled it out to:<BR>\n" );
document.write( "2A^2=A^2+500A+40,000 I am not sure how to solve for A or if that is even the correct variable. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #354531 by </B><A HREF=/tutors/aboutme.mpl?userid=neatmath><B>neatmath(302)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=neatmath><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=neatmath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=354531\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><font face=\"Tahoma\">You have 3 possible variables to work with:<br>\r<BR>\n" );
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document.write( "l length of rect field<br>\r<BR>\n" );
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document.write( "w width of rect field<br>\r<BR>\n" );
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document.write( "s side of square field<br>\r<BR>\n" );
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document.write( "We know:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l=400%2Bs ALIGN=MIDDLE  ALT=\"l=400%2Bs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=100%2Bs ALIGN=MIDDLE  ALT=\"w=100%2Bs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l%2Aw=2%2As%5E2 ALIGN=MIDDLE  ALT=\"l%2Aw=2%2As%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Now let's substitute those first 2 values for l and w into our 3rd equation:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28400%2Bs%29%2A%28100%2Bs%29=2%2As%5E2 ALIGN=MIDDLE  ALT=\"%28400%2Bs%29%2A%28100%2Bs%29=2%2As%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40000%2B100s%2B400s%2Bs%5E2=2%2As%5E2 ALIGN=MIDDLE  ALT=\"40000%2B100s%2B400s%2Bs%5E2=2%2As%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40000%2B500s%2Bs%5E2=2%2As%5E2 ALIGN=MIDDLE  ALT=\"40000%2B500s%2Bs%5E2=2%2As%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2-500s-40000=0 ALIGN=MIDDLE  ALT=\"s%5E2-500s-40000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Then we can factor this or use the quadratic formula:<br>\r<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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=1x%5E2%2B-500x%2B-40000+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-500x%2B-40000+=+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=%28-500%29%5E2-4%2A1%2A-40000=410000 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-500%29%5E2-4%2A1%2A-40000=410000\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=410000 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--500%2B-sqrt%28+410000+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--500%2B-sqrt%28+410000+%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-%28-500%29%2Bsqrt%28+410000+%29%29%2F2%5C1+=+570.156211871642 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-500%29%2Bsqrt%28+410000+%29%29%2F2%5C1+=+570.156211871642\"   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-%28-500%29-sqrt%28+410000+%29%29%2F2%5C1+=+-70.1562118716424 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-500%29-sqrt%28+410000+%29%29%2F2%5C1+=+-70.1562118716424\"   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=1x%5E2%2B-500x%2B-40000 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-500x%2B-40000\"   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=1x%5E2%2B-500x%2B-40000+=+%28x-570.156211871642%29%2A%28x--70.1562118716424%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-500x%2B-40000+=+%28x-570.156211871642%29%2A%28x--70.1562118716424%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 570.156211871642, -70.1562118716424.\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%2B-500%2Ax%2B-40000+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-500%2Ax%2B-40000+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "<br>\r<BR>\n" );
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document.write( "So your equation was right, you just needed to go a bit further.<br>\r<BR>\n" );
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document.write( "After using the quadratic formula, we can see there is only one possible answer for s:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=570.156 ALIGN=MIDDLE  ALT=\"s=570.156\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters rounded to 3 decimal places<br>\r<BR>\n" );
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document.write( "We had to discard the other possible solution because it was negative, and we can't have negative distances (in most cases).\r<BR>\n" );
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document.write( "And once we know the value for s, we can easily calculate the values for l and w.<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l=970.156 ALIGN=MIDDLE  ALT=\"l=970.156\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=670.156 ALIGN=MIDDLE  ALT=\"w=670.156\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters<br>\r<BR>\n" );
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document.write( "I hope this helps!<br> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );