document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997512>Question 997512</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A prism has congruent isosceles triangle for 2 of its faces. The ratio of one of the equal sides of one triangle to its base to the long edge of the prism is 5:8:9. The total volume of the solid is 6,912 cubic centimeter.\r<BR>\n" );
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document.write( "1. What is the perimeter of one triangle face?<BR>\n" );
document.write( "2. What is the surface area of the entire solid? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615578 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=615578\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equal legs of the isosceles triangle = 5x<BR>\n" );
document.write( "base of the isosceles triangle = 8x<BR>\n" );
document.write( "height of the isosceles triangle becomes 3x.<BR>\n" );
document.write( "this is derived by dropping a perpendicular from the vertex of the isosceles triangle to its base which splits the base into 2 equal segments of 4x each.<BR>\n" );
document.write( "solve for the height of the isosceles triangle by using one of the right triangles formed and pythagorus formula to get:<BR>\n" );
document.write( "(4x)^2 + h^2 = (5x)^2 which becomes:<BR>\n" );
document.write( "16x^2 + h^2 = 25x^2<BR>\n" );
document.write( "solve for h^2 to get h^2 = 9x^2<BR>\n" );
document.write( "solve for h to get h = 3x.\r<BR>\n" );
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document.write( "now you can find the area of each isosceles triangle.<BR>\n" );
document.write( "area = 1/2 * b * h which becomes:<BR>\n" );
document.write( "area = 1/2 * 8x * 3x which becomes:<BR>\n" );
document.write( "area = 12x^2.\r<BR>\n" );
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document.write( "the volume of the prism is equal to the area of the base * the height.<BR>\n" );
document.write( "the height of the prism is 9x.<BR>\n" );
document.write( "volume is equal to 12x^2 * 9x = 108x^3.<BR>\n" );
document.write( "since the volume of the prism is given as 6912, the formula becomes:<BR>\n" );
document.write( "6912 = 108x^3.<BR>\n" );
document.write( "solve for x to get x = 4.\r<BR>\n" );
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document.write( "the perimeter of one triangle face is equal to 5x + 8x + 5x = 18x.<BR>\n" );
document.write( "x = 4, so the perimeter of one triangle face is equal to 18 * 4 = 72 centimeters.\r<BR>\n" );
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document.write( "the surface area of the prism is the sum of the area of both triangular faces plus the sum of the area of the 3 rectangular faces.\r<BR>\n" );
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document.write( "each triangular face has an area of 1/2 * 3x * 8x = 1/2 * 3 * 4 * 8 * 4 = 1/2 * 12 * 32 = 6 * 32 = 192 square centimeters.\r<BR>\n" );
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document.write( "two triangular faces have a total surface area of 192 * 2 = 384 square centimeters.\r<BR>\n" );
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document.write( "2 of the rectangular faces have an area of 9x * 5x each = 45x^2 45 * 4^2 = 45*16 = 720 square centimeters each * 2 = 1440 square centimeters.\r<BR>\n" );
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document.write( "the third rectangular face has an area of 9x * 8x = 72x^2 = 72 * 4^2 = 72 * 16 = 1152 square centimeters.\r<BR>\n" );
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document.write( "total surface area = 384 + 1440 + 1152 = 2976 square centimeters.\r<BR>\n" );
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document.write( "your solution is:\r<BR>\n" );
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document.write( "the perimeter of one triangular face = 72 centimeters.\r<BR>\n" );
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document.write( "the surface area of the prism = 2976 square centimeters.\r<BR>\n" );
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document.write( "here's a diagram that might help you to understand.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/101903.jpg\" alt=\"$$$\" </> </SPAN>\n" );
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