document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=911998>Question 911998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In rectangle ABCD, a point M is selected inside the rectangle. If AM=4, BM=5, and CM=6, find the length of DM. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553803 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=553803\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the coordinates of A be (0,0).<BR>\n" );
document.write( "Then B would be (0,xb), C would be (xc,yc), and D would be (xd,0).<BR>\n" );
document.write( "Calculate the distance from each vertex to M.<BR>\n" );
document.write( "AM:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-0%29%5E2%2B%28y-0%29%5E2=16 ALIGN=MIDDLE  ALT=\"%28x-0%29%5E2%2B%28y-0%29%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=16 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "BM:<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-0%29%5E2%2B%28y-yb%29%5E2=25 ALIGN=MIDDLE  ALT=\"%28x-0%29%5E2%2B%28y-yb%29%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "CM:<BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-xc%29%5E2%2B%28y-yc%29%5E2=36 ALIGN=MIDDLE  ALT=\"%28x-xc%29%5E2%2B%28y-yc%29%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "DM:<BR>\n" );
document.write( "4.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-xd%29%5E2%2By%5E2=%28alpha%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-xd%29%5E2%2By%5E2=%28alpha%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the unknown distance.<BR>\n" );
document.write( "First we can simplify since,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=yb=yc ALIGN=MIDDLE  ALT=\"yb=yc\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xc=xd ALIGN=MIDDLE  ALT=\"xc=xd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,  for CM,<BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-xc%29%5E2%2B%28y-yb%29%5E2=36 ALIGN=MIDDLE  ALT=\"%28x-xc%29%5E2%2B%28y-yb%29%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and for DM,<BR>\n" );
document.write( "4.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-xc%29%5E2%2By%5E2=%28alpha%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-xc%29%5E2%2By%5E2=%28alpha%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting from 3 into 4.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2836-%28y-yb%29%5E2%29%2By%5E2=%28alpha%29%5E2 ALIGN=MIDDLE  ALT=\"%2836-%28y-yb%29%5E2%29%2By%5E2=%28alpha%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then substituting from 2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36-%2825-x%5E2%29%2By%5E2=%28alpha%29%5E2 ALIGN=MIDDLE  ALT=\"36-%2825-x%5E2%29%2By%5E2=%28alpha%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=11%2B%28x%5E2%2By%5E2%29=%28alpha%29%5E2 ALIGN=MIDDLE  ALT=\"11%2B%28x%5E2%2By%5E2%29=%28alpha%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Finally, substituting from 1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2B16=%28alpha%29%5E2 ALIGN=MIDDLE  ALT=\"11%2B16=%28alpha%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=alpha%5E2=27 ALIGN=MIDDLE  ALT=\"alpha%5E2=27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=sqrt%2827%29 ALIGN=MIDDLE  ALT=\"alpha=sqrt%2827%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DM=3sqrt%283%29 ALIGN=MIDDLE  ALT=\"DM=3sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C10%2C-10%2C10%2Ccircle%28-5%2C-5%2C0.2%29%2Ccircle%28-5%2C5%2C0.2%29%2Ccircle%287%2C5%2C0.2%29%2Ccircle%287%2C-5%2C0.2%29%2Ccircle%280%2C-1%2C0.2%29%2Cline%28-5%2C-5%2C-5%2C5%29%2Cline%28-5%2C5%2C7%2C5%29%2Cline%287%2C5%2C7%2C-5%29%2Cline%287%2C-5%2C-5%2C-5%29%2C%0D%0Alocate%28-5.5%2C7%2CB%29%2C%0D%0Alocate%28-5.5%2C-6%2CA%29%2C%0D%0Alocate%287%2C7%2CC%29%2C%0D%0Alocate%287%2C-6%2CD%29%2C%0D%0Alocate%280%2C1%2CM%29%2C%0D%0Ablue%28line%28-5%2C-5%2C0%2C-1%29%29%2C%0D%0Ablue%28line%28-5%2C5%2C0%2C-1%29%29%2C%0D%0Ablue%28line%287%2C5%2C0%2C-1%29%29%2C%0D%0Agreen%28line%287%2C-5%2C0%2C-1%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );