document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131761>Question 1131761</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given: &#8710;ABC –iso. &#8710;, m&#8736;BAC = 120° <BR>\n" );
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document.write( "AH<BR>\n" );
document.write( "  &#8869; <BR>\n" );
document.write( "BC<BR>\n" );
document.write( " , <BR>\n" );
document.write( "HD<BR>\n" );
document.write( " &#8869; <BR>\n" );
document.write( "AC<BR>\n" );
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document.write( "       AD = a cm, HD = b cm<BR>\n" );
document.write( "       Find: P&#8710;ADH </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748428 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=748428\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "   This is really an exercise in learning about what information is actually needed and what can be ignored. We don't care that 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;\" > is an isosceles triangles. \r<BR>\n" );
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document.write( "All that matters is noticing that triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ADH ALIGN=MIDDLE  ALT=\"ADH\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=right ALIGN=MIDDLE  ALT=\"right\"   DISABLED_style= \"max-width:90%; height:auto;\" > triangle with side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD ALIGN=MIDDLE  ALT=\"AD\"   DISABLED_style= \"max-width:90%; height:auto;\" > having a length of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm, and side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=HD ALIGN=MIDDLE  ALT=\"HD\"   DISABLED_style= \"max-width:90%; height:auto;\" > having a length of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm. \r<BR>\n" );
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document.write( "So you can use the Pythagorean theorem to calculate the length of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hypotenuse ALIGN=MIDDLE  ALT=\"hypotenuse\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AH ALIGN=MIDDLE  ALT=\"AH\"   DISABLED_style= \"max-width:90%; height:auto;\" > and from there, calculate the perimeter. \r<BR>\n" );
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document.write( "So: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AH+=+sqrt%28a%5E2+%2B+b%5E2%29 ALIGN=MIDDLE  ALT=\"AH+=+sqrt%28a%5E2+%2B+b%5E2%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=P ALIGN=MIDDLE  ALT=\"P\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8710; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ADH+=+AD+%2B+HD+%2B+AH ALIGN=MIDDLE  ALT=\"ADH+=+AD+%2B+HD+%2B+AH\"   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=P ALIGN=MIDDLE  ALT=\"P\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8710; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ADH+=+a+%2B+b+%2B+sqrt%28a%5E2+%2B+b%5E2%29 ALIGN=MIDDLE  ALT=\"ADH+=+a+%2B+b+%2B+sqrt%28a%5E2+%2B+b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Now the above is a \"correct\" answer, but we can take advantage of the extra information that was provided and determine that not only is triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ADH+ ALIGN=MIDDLE  ALT=\"ADH+\"   DISABLED_style= \"max-width:90%; height:auto;\" >a right triangle, but that it's a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F60%2F90+ ALIGN=MIDDLE  ALT=\"30%2F60%2F90+\"   DISABLED_style= \"max-width:90%; height:auto;\" >triangle. With that extra knowledge, we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD ALIGN=MIDDLE  ALT=\"AD\"   DISABLED_style= \"max-width:90%; height:auto;\" > is half the length of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=HA ALIGN=MIDDLE  ALT=\"HA\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "So we can simplify the length of the perimeter to: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+%2B+2a+=+3a+%2B+b ALIGN=MIDDLE  ALT=\"a+%2B+b+%2B+2a+=+3a+%2B+b\"   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=P ALIGN=MIDDLE  ALT=\"P\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8710; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ADH+=3a+%2B+b ALIGN=MIDDLE  ALT=\"ADH+=3a+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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