document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=932918>Question 932918</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the length of the longest stick that will fit in a 4 cm by 6 cm by 12 cm box. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #566588 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=566588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The length (in cm) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%5E2%2B6%5E2%2B12%5E2%29%2Bsqrt%2816%0D%0A36%2B144%29=sqrt%28196%29=highlight%2814%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "THE EXPLANATION:<BR>\n" );
document.write( "Let's say the box is sitting on one of the rectangular sides that measure 6 cm by 12 cm.<BR>\n" );
document.write( "We call that the base of the box.<BR>\n" );
document.write( "The diagonal splits that base into 2 right triangles with legs measuring 6 cm by 12 cm.<BR>\n" );
document.write( "The length of that diagonal, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28d%29 ALIGN=MIDDLE  ALT=\"green%28d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm, according to the Pythagorean theorem, is such that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28d%29%5E2=6%5E2%2B12%5E2 ALIGN=MIDDLE  ALT=\"green%28d%29%5E2=6%5E2%2B12%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C150%2C-2%2C13%2C-1%2C6.5%2C%0D%0Arectangle%280%2C0%2C12%2C6%29%2Crectangle%280%2C0%2C0.5%2C0.5%29%2C%0D%0Agreen%28line%280%2C6%2C12%2C0%29%29%2C%0D%0Alocate%280.05%2C3.2%2C6cm%29%2Clocate%285.8%2C0.7%2C12cm%29%2C%0D%0Alocate%285.8%2C3%2Cgreen%28d%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That diagonal is perpendicular to one of the vertical 4-cm long edges of the box.<BR>\n" );
document.write( "The longest possible stick, of length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28s%29 ALIGN=MIDDLE  ALT=\"red%28s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm, stick will form a right triangle with the diagonal of the base and a vertical edge.<BR>\n" );
document.write( "This is what the (see through) box looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28360%2C180%2C-2%2C16%2C-1%2C8%2C%0D%0Arectangle%280%2C3%2C12%2C7%29%2Ctriangle%2814%2C0%2C0%2C3%2C12%2C3%29%2C%0D%0Aline%282%2C0%2C14%2C0%29%2Cline%282%2C4%2C14%2C4%29%2Cline%280%2C7%2C12%2C7%29%2C%0D%0Aline%282%2C0%2C2%2C4%29%2Cline%2814%2C0%2C14%2C4%29%2Cline%280%2C3%2C0%2C7%29%2C%0D%0Aline%280%2C3%2C2%2C0%29%2Cline%2812%2C7%2C14%2C4%29%2Cline%280%2C7%2C2%2C4%29%2C%0D%0Agreen%28line%280%2C3%2C14%2C0%29%29%2Cred%28line%280%2C3%2C14%2C4%29%29%2C%0D%0Alocate%28-0.3%2C1.8%2C6cm%29%2Clocate%287.8%2C0%2C12cm%29%2C%0D%0Alocate%287%2C1.5%2Cgreen%28d%29%29%2Clocate%288.5%2C3.8%2Cred%28s%29%29%2C%0D%0Alocate%2814.05%2C2.5%2C4cm%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "According to the Pythagorean theorem,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28s%29%5E2=4%5E2%2Bgreen%28d%29%5E2 ALIGN=MIDDLE  ALT=\"red%28s%29%5E2=4%5E2%2Bgreen%28d%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=red%28s%29%5E2=4%5E2%2B6%5E2%2B12%5E2 ALIGN=MIDDLE  ALT=\"red%28s%29%5E2=4%5E2%2B6%5E2%2B12%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28s%29=sqrt%284%5E2%2B6%5E2%2B12%5E2%29 ALIGN=MIDDLE  ALT=\"red%28s%29=sqrt%284%5E2%2B6%5E2%2B12%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );