document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109661>Question 1109661</A>: <I><SPAN STYLE=\"word-break: break-all;\"> -find the longest stick that can be placed inside a rectangles with sides 4cm and 9cm?\r<BR>\n" );
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document.write( "-find the perimeter of the square with vertices A(2,3),B(-1,5),C(-5,1) & D(-1,-3)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724640 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=724640\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The longest stick that can be placed inside a rectangles with sides 4cm and 9cm<BR>\n" );
document.write( "is a hair-thin stick as long as the diagonal of the rectangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C200%2C-0.3%2C9.7%2C-0.7%2C4.3%2C%0D%0Arectangle%280%2C0%2C0.3%2C0.3%29%2Crectangle%289%2C0%2C8.7%2C0.3%29%2C%0D%0Arectangle%280%2C4%2C0.3%2C3.7%29%2Cline%280%2C0%2C9%2C0%29%2C%0D%0Aline%280%2C4%2C9%2C4%29%2Cline%280%2C0%2C0%2C4%29%2Cline%289%2C0%2C9%2C4%29%2C%0D%0Ared%28line%280%2C0%2C9%2C4%29%29%2Clocate%284.5%2C2%2Cred%28stick%29%29%2C%0D%0Alocate%284%2C0%2C9cm%29%2Clocate%289.1%2C2.2%2C4cm%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "According to the Pythagorean theorem, the length of that stick is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%289cm%29%5E2%2B%284cm%29%5E2%29=sqrt%2881cm%5E2%2B16cm%5E2%29=sqrt%2897cm%5E2%29=sqrt%2897%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm ALIGN=MIDDLE  ALT=\"cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9.8cm ALIGN=MIDDLE  ALT=\"9.8cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( " <BR>\n" );
document.write( "The points A(2,3), B(-1,5), C(-5,1) & D(-1,-3), shown on the sketch below,<BR>\n" );
document.write( "do not determine a square.<BR>\n" );
document.write( "They are vertices of a quadrilateral with no parallel sides,<BR>\n" );
document.write( "Points P(3,1), B(-1,5), C(-5,1) & D(-1,-3) are the vertices of a square,<BR>\n" );
document.write( "with PC and BD being its diagonals.<BR>\n" );
document.write( "They are equally long, perpendicular, and bisect each other,<BR>\n" );
document.write( "and that tells us PBCD is a square.<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-6%2C4%2C-4%2C6%2Cgrid%281%29%2C%0D%0Ared%28circle%282%2C3%2C0.1%29%29%2Cred%28circle%28-1%2C5%2C0.1%29%29%2C%0D%0Ared%28circle%28-5%2C1%2C0.1%29%29%2Cred%28circle%28-1%2C-3%2C0.1%29%29%2C%0D%0Alocate%282.1%2C3%2CA%29%2Clocate%28-0.9%2C5%2CB%29%2C%0D%0Alocate%28-4.9%2C1%2CC%29%2Clocate%28-0.9%2C-3%2CD%29%2C%0D%0Agreen%28circle%283%2C1%2C0.1%29%29%2Cgreen%28circle%283%2C1%2C0.15%29%29%2C%0D%0Alocate%283.1%2C1%2CP%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The lengths of the sides of ABCD are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=sqrt%28%285-3%29%5E2%2B%28-1-2%29%5E2%29=sqrt%282%5E2%2B%28-3%29%5E2%29=sqrt%284%2B9%29=sqrt%2813%29=about3.6 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=sqrt%28%281-5%29%5E2%2B%28-5-%28-1%29%29%5E2%29=sqrt%28%28-4%29%5E2%2B%28-4%29%5E2%29=sqrt%2816%2B16%29=sqrt%2832%29=4sqrt%282%29=about5.7 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD=sqrt%28%28-3-1%29%5E2%2B%28-1-%28-5%29%29%5E2%29=sqrt%28%28-4%29%5E2%2B4%5E2%29=sqrt%2816%2B16%29=sqrt%2832%29=4sqrt%282%29=about5.7 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DA=sqrt%28%283-%28-3%29%29%5E2%2B%282-%28-1%29%29%5E2%29=sqrt%286%5E2%2B3%5E2%29=sqrt%2836%2B9%29=sqrt%2845%29=3sqrt%285%29=about6.7 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The perimeter of ABCD is approximately<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%2BBC%2BCD%2BDA=3.6%2B5.7%2B5.7%2B6.7=21.7 ALIGN=MIDDLE  ALT=\"AB%2BBC%2BCD%2BDA=3.6%2B5.7%2B5.7%2B6.7=21.7\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The exact result is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2813%29%2B8sqrt%282%29%2B3sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%2813%29%2B8sqrt%282%29%2B3sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If we use approximate side lengths with more decimal places,<BR>\n" );
document.write( "we realize that the unrounded result is closer to 21.6:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%2BBC%2BCD%2BDA=3.605551%2B5.656854%2B5.656854%2B6.708204=21.627463 ALIGN=MIDDLE  ALT=\"AB%2BBC%2BCD%2BDA=3.605551%2B5.656854%2B5.656854%2B6.708204=21.627463\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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