document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=604437>Question 604437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Right triangle ABC with legs AB= 9 millimeters and BC= 12 millimeters is the base of a right prism that has a surface area of 450 square millimeters. What is the height of the prism? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #381205 by </B><A HREF=/tutors/aboutme.mpl?userid=alicealc><B>alicealc(293)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=alicealc><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=381205\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume that AB is perpendicular to BC<BR>\n" );
document.write( "because it's a triangle, then area of triangle:<BR>\n" );
document.write( "Area = 1/2 * base * height<BR>\n" );
document.write( "Area = 1/2 * 12 * 9 = 6 * 9 = 54 square milimeters\r<BR>\n" );
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document.write( "because it's a right triangle, then we can use Phytagoras theorem to find the other side of the triangle:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%5E2+%2B+BC%5E2+=+AC%5E2 ALIGN=MIDDLE  ALT=\"AB%5E2+%2B+BC%5E2+=+AC%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E2+%2B+12%5E2+=+AC%5E2 ALIGN=MIDDLE  ALT=\"9%5E2+%2B+12%5E2+=+AC%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E2+%2B+12%5E2+=+AC%5E2 ALIGN=MIDDLE  ALT=\"9%5E2+%2B+12%5E2+=+AC%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81+%2B+144+=+AC%5E2 ALIGN=MIDDLE  ALT=\"81+%2B+144+=+AC%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225+=+AC%5E2 ALIGN=MIDDLE  ALT=\"225+=+AC%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC+=+sqrt%28225%29 ALIGN=MIDDLE  ALT=\"AC+=+sqrt%28225%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "AC = 15 milimeters\r<BR>\n" );
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document.write( "Surface Area (SA) of a prism:<BR>\n" );
document.write( "SA = 2*base area + base perimeter*prism's height<BR>\n" );
document.write( "450 = 2*54 + (9 + 12 + 15)*prism's height<BR>\n" );
document.write( "450 = 108 + 36*prism's height<BR>\n" );
document.write( "450 - 108 = 36*prism's height<BR>\n" );
document.write( "342 = 36 * prism's height<BR>\n" );
document.write( "prism's height = 342/36 = 9.5 milimeters\r<BR>\n" );
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document.write( "so, the height of the prism is 9.5 millimeters </SPAN>\n" );
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