document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=540938>Question 540938</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the altitude of this equilateral triangle if it only equals 8  on the bottom of the triangle enter your answer as a simplified radical  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #354036 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=354036\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Equilateral triangles are very symmetrical. In an equilateral triangle, all three sides have the same length and all 3 angles have the same measure (60 degrees).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+250%2C+150%2C+-10%2C+10%2C+-2%2C+10%2C%0D%0A++locate%28+0%2C+0%2C+P+%29%2C%0D%0A++locate%28+-5%2C+0%2C+A+%29%2C+locate%28+5%2C+0%2C+B+%29%2C+locate%28+0%2C+10%2C+C+%29%2C%0D%0A++blue%28line%28+5%2C+0%2C+-5%2C+0+%29%29%2C%0D%0A++line%28+5%2C+0%2C+0%2C+8.66+%29%2C%0D%0A++line%28+-5%2C+0%2C+0%2C+8.66%29%2C%0D%0A++red%28line%28+0%2C+0%2C+0%2C+8.66+%29%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >Being a symmetrical figure, the CP altitude bisects the base AB.<BR>\n" );
document.write( "So the length of each triangle side (AB, BC, and CA) is 8.<BR>\n" );
document.write( "The length of segment PB is half of the base length, so it's 4.<BR>\n" );
document.write( "Right triangle PBC has a hypotenuse (BC) of length 8, and one leg of length 4.<BR>\n" );
document.write( "We use Pythagoras theorem to find the length of the other leg (altitude CP).<BR>\n" );
document.write( "Let's call that length x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4%5E2=8%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B4%5E2=8%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B16=64 ALIGN=MIDDLE  ALT=\"x%5E2%2B16=64\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=64-16 ALIGN=MIDDLE  ALT=\"x%5E2=64-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=48 ALIGN=MIDDLE  ALT=\"x%5E2=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the length of a segment must be a positive number, never a negative one, there is only one solution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%2848%29=sqrt%2816%2A3%29=sqrt%2816%29%2Asqrt%283%29=4sqrt%283%29 ALIGN=MIDDLE  ALT=\"x=sqrt%2848%29=sqrt%2816%2A3%29=sqrt%2816%29%2Asqrt%283%29=4sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );