document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1064751>Question 1064751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the height of an equilateral triangle is also a root of equation y^4-3y^2-270 then the area of the triangle in cm^2 is  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #679834 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=679834\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y^4-3y^2-270=0<BR>\n" );
document.write( "(y^2-18)(y^2+15)=0<BR>\n" );
document.write( "y^2=18; y^2=-15, can exclude.<BR>\n" );
document.write( "y=3 sqrt (2), only positive root\r<BR>\n" );
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document.write( "equilateral triangle has sides s<BR>\n" );
document.write( "height is (s/2)sqrt(3)=3 sqrt (2)<BR>\n" );
document.write( "Therefore, side is 6sqrt(2)/sqrt(3)<BR>\n" );
document.write( "That is 6 sqrt(6)/3 by rationalizing, or 2 sqrt(6)<BR>\n" );
document.write( "The area is 1/2 bh=1/2 *2 sqrt(6)*3 sqrt (2)=3 sqrt (12)=6*sqrt (3)\r<BR>\n" );
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document.write( "The area of an equilateral triangle with side s is s^2/4*(sqrt3)<BR>\n" );
document.write( "Here, s^2=(2 sqrt(6))^2=4*6=24<BR>\n" );
document.write( "Area is 24/4* (sqrt 3)=6 sqrt (3)<BR>\n" );
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