document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=909429>Question 909429</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A triangle has side lengths measuring 30, 40, and 50 units. What is the length of its shortest altitude, in units? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #551870 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=551870\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "A triangle has side lengths measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=30 ALIGN=MIDDLE  ALT=\"a=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=40 ALIGN=MIDDLE  ALT=\"b=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=50 ALIGN=MIDDLE  ALT=\"c=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > units is an right angle triangle.\r<BR>\n" );
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document.write( "In a right triangle the three altitudes are: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Ba%5D ALIGN=MIDDLE  ALT=\"h%5Ba%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Bb%5D%2C+and+%7B%7B%7Bh%5Bc%5D ALIGN=MIDDLE  ALT=\"h%5Bb%5D%2C+and+%7B%7B%7Bh%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the first two of which equal the leg lengths <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > respectively) and they are related according to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fh%5Ba%5D%5E2%2B1%2Fh%5Bb%5D%5E2=1%2F+h%5Bc%5D%5E2 ALIGN=MIDDLE  ALT=\"1%2Fh%5Ba%5D%5E2%2B1%2Fh%5Bb%5D%5E2=1%2F+h%5Bc%5D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Ba%5D=30 ALIGN=MIDDLE  ALT=\"h%5Ba%5D=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Bb%5D=40 ALIGN=MIDDLE  ALT=\"h%5Bb%5D=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Bc%5D ALIGN=MIDDLE  ALT=\"h%5Bc%5D\"   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%2F30%5E2%2B1%2F40%5E2=1%2F+h%5Bc%5D%5E2 ALIGN=MIDDLE  ALT=\"1%2F30%5E2%2B1%2F40%5E2=1%2F+h%5Bc%5D%5E2\"   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%2F900%2B1%2F1600=1%2F+h%5Bc%5D%5E2 ALIGN=MIDDLE  ALT=\"1%2F900%2B1%2F1600=1%2F+h%5Bc%5D%5E2\"   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=1600%2F1440000%2B900%2F1440000=1%2F+h%5Bc%5D%5E2 ALIGN=MIDDLE  ALT=\"1600%2F1440000%2B900%2F1440000=1%2F+h%5Bc%5D%5E2\"   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=%281600%2B900%29%2F1440000=1%2F+h%5Bc%5D%5E2 ALIGN=MIDDLE  ALT=\"%281600%2B900%29%2F1440000=1%2F+h%5Bc%5D%5E2\"   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=25cross%280%29cross%280%29%2F14400cross%280%29cross%280%29=1%2F+h%5Bc%5D%5E2 ALIGN=MIDDLE  ALT=\"25cross%280%29cross%280%29%2F14400cross%280%29cross%280%29=1%2F+h%5Bc%5D%5E2\"   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=25%2F14400=1%2F+h%5Bc%5D%5E2 ALIGN=MIDDLE  ALT=\"25%2F14400=1%2F+h%5Bc%5D%5E2\"   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=cross%2825%291%2Fcross%2814400576%29=1%2F+h%5Bc%5D%5E2 ALIGN=MIDDLE  ALT=\"cross%2825%291%2Fcross%2814400576%29=1%2F+h%5Bc%5D%5E2\"   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%2F576=1%2F+h%5Bc%5D%5E2 ALIGN=MIDDLE  ALT=\"1%2F576=1%2F+h%5Bc%5D%5E2\"   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=h%5Bc%5D%5E2=576 ALIGN=MIDDLE  ALT=\"h%5Bc%5D%5E2=576\"   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=h%5Bc%5D=sqrt%28576%29 ALIGN=MIDDLE  ALT=\"h%5Bc%5D=sqrt%28576%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=h%5Bc%5D=24 ALIGN=MIDDLE  ALT=\"h%5Bc%5D=24\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...so, this is the length of shortest altitude\r<BR>\n" );
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