document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936442>Question 936442</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is a geometric mean? Explain the different triangle and similarity relationships of the geometric mean.\r<BR>\n" );
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document.write( "I know that Geometric Mean is a special average where I would multiply numbers together then take their square root (if only two numbers), cube root (if three numbers) and so forth and so on. (But I'm having trouble answering the second part of the question please help.)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #570166 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=570166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) Geometric mean is the nth root of the product of n numbers.<BR>\n" );
document.write( "b) Consider a right triangle ABC with angle c = 90 degrees.  Drop an altitude(a) from angle c to point D on line segment AC.  Now we have two right triangles that are similar, ABD and DBC.  Also, we choose AD = 4 and DC = 11 and AC is the hypotenuse of ABC.  Since the triangles are similar, we have the following relationship involving the two triangles.<BR>\n" );
document.write( "4/a = a/11<BR>\n" );
document.write( "a^2 = 44<BR>\n" );
document.write( "a = 2*square root(11)<BR>\n" );
document.write( "note that a is the geometric mean of AD(4) and DC(11), that is<BR>\n" );
document.write( "a = square root(44) = 2*square root(11)\r<BR>\n" );
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document.write( "   </SPAN>\n" );
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