document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123348>Question 1123348</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In isosceles &#9651;ABC (AC = BC) with base angle 30° CD is a median. How long is the leg of &#9651;ABC, if sum of the perimeters of &#9651;ACD and &#9651;BCD is 20cm more than the perimeter of &#9651;ABC?     <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739712 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=739712\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Draw this one.  Let the equal legs be x, so median is 0.5x (30-60-90 triangle) and the third leg of the bisected triangle is 0.5x sqrt (3)<BR>\n" );
document.write( "Perimeter of the two triangles is 2(3x+x sqrt(3))<BR>\n" );
document.write( "perimeter of the large triangle is 4x+2xsqrt (3)<BR>\n" );
document.write( "therefore, 6x+2x sqrt(3)-20=4x+2x sqrt(3)<BR>\n" );
document.write( "2x=20<BR>\n" );
document.write( "x=10 cm<BR>\n" );
document.write( "the sides of ABC are 20-20-10 sqrt (3) or 40+10 sqrt(3) or about 57.32<BR>\n" );
document.write( "each of the two triangles has perimeter 20-10-5 sqrt(3) or about 38.66.  Two of them have perimeter 77.32<BR>\n" );
document.write( "The last leg of ABC is 10 sqrt(3) cm or 17.32 cm. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );