document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065772>Question 1065772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A triangular pyramid has a lateral surface of 225 square centimeters. If the height of the pyramid is greater than 12 centimeters and the base has nine equal sides, what are whole-number possibilities for the height and width of each triangular face?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #680938 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=680938\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> lateral surface area doesn't include the area of the base.<BR>\n" );
document.write( "if there are 9 equal sides, then there are 9 equal triangles.<BR>\n" );
document.write( "that means the area of each triangle is 25 square centimeters.<BR>\n" );
document.write( "the formula for the area of a triangle is 1/2 * b * h.<BR>\n" );
document.write( "you get 1/2 * b * h = 25<BR>\n" );
document.write( "multiply both sides of this equation by 2 and you get b * h = 50<BR>\n" );
document.write( "divide both sides of this equation by h and you get b = 50 / h<BR>\n" );
document.write( "since b > 12, then 50 / h > 12.<BR>\n" );
document.write( "multiply both sides of this equation by h to get 50 > 12 * h.<BR>\n" );
document.write( "looks like h is a multiple of 12 and can be 1, 2, 3, or 4.<BR>\n" );
document.write( "it can't be 5 because 12 * 5 = 60 > 50.<BR>\n" );
document.write( "to test these out, use the formula of 25 = 1/2 * b * h and multiply both sides of it by 2 to get 50 = b * h.<BR>\n" );
document.write( "if b = 1, then h = 50 > 12 which is a whole number.<BR>\n" );
document.write( "if b = 2, then h = 25 > 12 which is a whole number.<BR>\n" );
document.write( "if b = 3, then h = 15 and 5/15 > 12 but is not a whole number.<BR>\n" );
document.write( "if b = 4, then h = 12 and 2/12 > 12 but is not a whole number.<BR>\n" );
document.write( "if b = 5, then h = 10 which is smaller than 12.<BR>\n" );
document.write( "my guess is that the base can either be 1 or 2.<BR>\n" );
document.write( "when 1, the height is 50.<BR>\n" );
document.write( "when 2, the height is 25.<BR>\n" );
document.write( "the area of each triangle is always 25.<BR>\n" );
document.write( "the lateral area is always 225.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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