document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=939227>Question 939227</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The triangle is isosceles and the perimeter equals 54 cm. The height is 3*sqrt(21). Find the lengths of the sides and the area of the triangle. Express your answers in simplest radical form. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #572290 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=572290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> definition of isosceles triangle: a triangle with two equal sides<BR>\n" );
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document.write( "the problem doesn't say which height is being talked about, so let's assume it's the height from the non-equal side (the base b), to the point where the two equal sides meet:<BR>\n" );
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document.write( "perimeter = 54 = 2s + b<BR>\n" );
document.write( "2s = 54 - b<BR>\n" );
document.write( "s = (54 - b)/2<BR>\n" );
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document.write( "length of the equal sides:<BR>\n" );
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document.write( "s = sqrt( hh + bb/4 )<BR>\n" );
document.write( "(54 - b)/2 = sqrt( hh + bb/4 )<BR>\n" );
document.write( "(54 - b)(54 - b)/4 = hh + bb/4<BR>\n" );
document.write( "54*54 - 108b + bb = 4hh + bb<BR>\n" );
document.write( "2916 - 108b = 4hh<BR>\n" );
document.write( "108b = 2916 - 4hh<BR>\n" );
document.write( "b = (2916 - 4hh)/108<BR>\n" );
document.write( "b = (2916 - 4* 3*sqrt(21) * 3*sqrt(21) )/108<BR>\n" );
document.write( "b = (2916 - 4*3*3*sqrt(21)*sqrt(21) )/108<BR>\n" );
document.write( "b = (2916 - 4*3*3*21 )/108<BR>\n" );
document.write( "b = 20 cm<BR>\n" );
document.write( "s = (54 - b)/2<BR>\n" );
document.write( "s = (54 - 20)/2<BR>\n" );
document.write( "s = 17 cm<BR>\n" );
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document.write( "area:<BR>\n" );
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document.write( "a = bh/2<BR>\n" );
document.write( "a = 20*3*sqrt(21)/2<BR>\n" );
document.write( "a = 30*sqrt(21) sq.cm<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );