document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140950>Question 1140950</A>: <I><SPAN STYLE=\"word-break: break-all;\"> BD is the altitude of right triangle ABC. If AD=3 and DC=12, what is the length of BD?\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 #761494 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=761494\">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=BD ALIGN=MIDDLE  ALT=\"BD\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the altitude of right triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC ALIGN=MIDDLE  ALT=\"ABC\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD=3+ ALIGN=MIDDLE  ALT=\"AD=3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DC=12 ALIGN=MIDDLE  ALT=\"DC=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, what is the length of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD ALIGN=MIDDLE  ALT=\"BD\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+20%2C+-10%2C+20%2C%0D%0Acircle%280%2C8%2C.12%29%2Clocate%280.5%2C8%2CA%29%2C%0D%0Acircle%280%2C0%2C.12%29%2Clocate%280.5%2C-0.5%2CB%29%2C%0D%0Acircle%280%2C12%2C.12%29%2Clocate%2812%2C0.5%2CC%29%2C%0D%0Aline%280%2C8%2C12%2C0%29%2Cline%280%2C0%2C3%2C6%29%2C%0D%0Acircle%283%2C6%2C.12%29%2Clocate%283%2C6%2CD%29%2Clocate%282%2C7.5%2C3%29%2Clocate%286%2C5%2C12%29%2C%0D%0Alocate%280.5%2C1%2C1%29%2Clocate%280.2%2C1.5%2C2%29%2Clocate%280.2%2C7%2C1%29%2Clocate%2810%2C0.7%2C2%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+20%2C+-10%2C+20%2C+0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "given:  right triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC ALIGN=MIDDLE  ALT=\"ABC\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+90 ALIGN=MIDDLE  ALT=\"B+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >°  and altitude divides angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > into two angles ,  < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+ ALIGN=MIDDLE  ALT=\"2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> <<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+2+=+90 ALIGN=MIDDLE  ALT=\"1+%2B+2+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >°  ……(1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD ALIGN=MIDDLE  ALT=\"BD\"   DISABLED_style= \"max-width:90%; height:auto;\" > is perpendicular to<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+AC+ ALIGN=MIDDLE  ALT=\"+AC+\"   DISABLED_style= \"max-width:90%; height:auto;\" >( given)\r<BR>\n" );
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document.write( "=> <<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > + < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DCB+=+90 ALIGN=MIDDLE  ALT=\"DCB+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >° …….(2)\r<BR>\n" );
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document.write( "=> < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DCB+ ALIGN=MIDDLE  ALT=\"DCB+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ………….by (1) & (2)\r<BR>\n" );
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document.write( "& < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BAD ALIGN=MIDDLE  ALT=\"BAD\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, triangle<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+BCD ALIGN=MIDDLE  ALT=\"+BCD\"   DISABLED_style= \"max-width:90%; height:auto;\" > ~ triangle<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ABD ALIGN=MIDDLE  ALT=\"+ABD\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( by AAA similarity theorem)\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%2FAB+=+CD%2FBD+=+BD%2FAD ALIGN=MIDDLE  ALT=\"BC%2FAB+=+CD%2FBD+=+BD%2FAD\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( corresponding sides of similar triangles)\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%2FAB+=+12%2FBD+=+BD%2F3 ALIGN=MIDDLE  ALT=\"BC%2FAB+=+12%2FBD+=+BD%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD%5E2+=+36 ALIGN=MIDDLE  ALT=\"BD%5E2+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD+=+sqrt%2836%29 ALIGN=MIDDLE  ALT=\"BD+=+sqrt%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD+=+6 ALIGN=MIDDLE  ALT=\"BD+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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