document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1068663>Question 1068663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Wanda is trying to locate the Fermat point P of triangle ABC, where A is at the origin, B is at (10,0), and C is at (3,5) (the Fermat point is the point such that the sum of its distances from the vertices of a triangle is minimized). She guesses that the point is at P = (4,2), and computes the sum of the distances from P to the vertices of triangle ABC. If she obtains <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2Asqrt%285%29+%2B+n%2Asqrt%2810%29+ ALIGN=MIDDLE  ALT=\"m%2Asqrt%285%29+%2B+n%2Asqrt%2810%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where m and n are integers, what is m + n?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #683912 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=683912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B1%5D%5E2=%284-0%29%5E2%2B%282-0%29%5E2 ALIGN=MIDDLE  ALT=\"D%5B1%5D%5E2=%284-0%29%5E2%2B%282-0%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B1%5D%5E2=20 ALIGN=MIDDLE  ALT=\"D%5B1%5D%5E2=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B1%5D=4sqrt%285%29 ALIGN=MIDDLE  ALT=\"D%5B1%5D=4sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B2%5D%5E2=%28-6%29%5E2%2B4 ALIGN=MIDDLE  ALT=\"D%5B2%5D%5E2=%28-6%29%5E2%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B2%5D%5E2=36%2B4 ALIGN=MIDDLE  ALT=\"D%5B2%5D%5E2=36%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B2%5D%5E2=40 ALIGN=MIDDLE  ALT=\"D%5B2%5D%5E2=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B2%5D=2sqrt%2810%29 ALIGN=MIDDLE  ALT=\"D%5B2%5D=2sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B3%5D%5E2=%284-3%29%5E2%2B%282-5%29%5E2 ALIGN=MIDDLE  ALT=\"D%5B3%5D%5E2=%284-3%29%5E2%2B%282-5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B3%5D%5E2=1%2B9 ALIGN=MIDDLE  ALT=\"D%5B3%5D%5E2=1%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B3%5D%5E2=10 ALIGN=MIDDLE  ALT=\"D%5B3%5D%5E2=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B3%5D=sqrt%2810%29 ALIGN=MIDDLE  ALT=\"D%5B3%5D=sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B1%5D%2BD%5B2%5D%2BD%5B3%5D=4%2Asqrt%285%29%2B2%2Asqrt%2810%29%2Bsqrt%2810%29=m%2Asqrt%285%29%2Bn%2Asqrt%2810%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now solve for m and n.<BR>\n" );
document.write( "And then add them to get the final answer.\r<BR>\n" );
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document.write( "By the way, the actual minimum occurs at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.34 ALIGN=MIDDLE  ALT=\"3.34\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.64 ALIGN=MIDDLE  ALT=\"2.64\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
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