document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151761>Question 151761</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hank has three square fields. One field is 1 kilometer longer than the side of the smallest field. The side of the largest field is 3 kilometers longer than the smallest field. The total area of the fields is 38 square kilometers . What is the area of each field? This doesn't sound like it should be difficult but I can't figure it out.  A=S^2    ????  38= S^2   +    S^2+1^2   + S^2 +3^2  ??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #112265 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=112265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It can get confusing.<BR>\n" );
document.write( "First name the sides of the fields.<BR>\n" );
document.write( "How about S for small field, L for large field, and M for the middle field.<BR>\n" );
document.write( "Since they're squares the area of each field is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BS%5D=S%5E2 ALIGN=MIDDLE  ALT=\"A%5BS%5D=S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BM%5D=M%5E2 ALIGN=MIDDLE  ALT=\"A%5BM%5D=M%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BL%5D=L%5E2 ALIGN=MIDDLE  ALT=\"A%5BL%5D=L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The largest field side is 3 km larger than the small field.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=S%2B3 ALIGN=MIDDLE  ALT=\"L=S%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "One field is 1 kilometer longer than the side of the smallest field. <BR>\n" );
document.write( "I'm assuming this is the middle field.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=S%2B1 ALIGN=MIDDLE  ALT=\"M=S%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The total area is 38 km^2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2%2BM%5E2%2BL%5E2=38 ALIGN=MIDDLE  ALT=\"S%5E2%2BM%5E2%2BL%5E2=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now substitute for M and L.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2%2BM%5E2%2BL%5E2=38 ALIGN=MIDDLE  ALT=\"S%5E2%2BM%5E2%2BL%5E2=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2%2B%28S%2B1%29%5E2%2B%28S%2B3%29%5E2=38 ALIGN=MIDDLE  ALT=\"S%5E2%2B%28S%2B1%29%5E2%2B%28S%2B3%29%5E2=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note the expansion of the squares. <BR>\n" );
document.write( "Check on the FOIL method if this isn't clear.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2%2Bhighlight%28S%5E2%2B2S%2B1%29%2Bhighlight%28S%5E2%2B6S%2B9%29=38 ALIGN=MIDDLE  ALT=\"S%5E2%2Bhighlight%28S%5E2%2B2S%2B1%29%2Bhighlight%28S%5E2%2B6S%2B9%29=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3S%5E2%2B8S%2B10=38 ALIGN=MIDDLE  ALT=\"3S%5E2%2B8S%2B10=38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3S%5E2%2B8S-28=0 ALIGN=MIDDLE  ALT=\"3S%5E2%2B8S-28=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can factor this quadratic equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283S%2B14%29%28S-2%29=0 ALIGN=MIDDLE  ALT=\"%283S%2B14%29%28S-2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3S%2B14=0 ALIGN=MIDDLE  ALT=\"3S%2B14=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=-14%2F3 ALIGN=MIDDLE  ALT=\"S=-14%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A negative length does not make sense in this case so we throw out that answer.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S-2=0 ALIGN=MIDDLE  ALT=\"S-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28S=2%29 ALIGN=MIDDLE  ALT=\"highlight%28S=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then from above,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=S%2B1 ALIGN=MIDDLE  ALT=\"M=S%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=2%2B1 ALIGN=MIDDLE  ALT=\"M=2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28M=3%29 ALIGN=MIDDLE  ALT=\"highlight%28M=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and finally<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=S%2B3 ALIGN=MIDDLE  ALT=\"L=S%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=2%2B3 ALIGN=MIDDLE  ALT=\"L=2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28L=5%29 ALIGN=MIDDLE  ALT=\"highlight%28L=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BS%5D=S%5E2=2%5E2=4 ALIGN=MIDDLE  ALT=\"A%5BS%5D=S%5E2=2%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BM%5D=M%5E2=3%5E2=9 ALIGN=MIDDLE  ALT=\"A%5BM%5D=M%5E2=3%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BL%5D=L%5E2=5%5E2=25 ALIGN=MIDDLE  ALT=\"A%5BL%5D=L%5E2=5%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The smallest field is 4 km^2, the middle field is 9 km^2, and the large field is 25 km^2.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );