document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255687>Question 255687</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A family needs a tent that measures at least 10m^3 and the tent (isosceles triangular prism) they have has a height of 2m, and a base length of 3m. However, the length is unknown, but the surface area outside the tent (including bottom) is 38m^2. Will the tent be big enough for them?\r<BR>\n" );
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document.write( "Thank you for your help... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187934 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=187934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A family needs a tent that measures at least 10m^3 and the tent (isosceles triangular prism) they have has a height of 2m, and a base length of 3m. However, the length is unknown, but the surface area outside the tent (including bottom) is 38m^2. Will the tent be big enough for them?\r<BR>\n" );
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document.write( "What is the volume of a tent with measurements:<BR>\n" );
document.write( "h=2m<BR>\n" );
document.write( "b=3m<BR>\n" );
document.write( "l=?<BR>\n" );
document.write( "SA (outside of tent)=38m^2 <BR>\n" );
document.write( "2 sides for the top, 1 side for bottom, 1 front, 1 back <BR>\n" );
document.write( "that is 5 sides<BR>\n" );
document.write( "front=back=(1/2)(3)(2)=(1/2)(6)=3 --> total SA front+back 6m^2 <BR>\n" );
document.write( "((1/2)b)^2+h^2=(width of one of the top sides)^2 let's call it slope^2<BR>\n" );
document.write( "((1/2)(3))^2+2^2<BR>\n" );
document.write( "1.5^2+4<BR>\n" );
document.write( "2.25+4<BR>\n" );
document.write( "6.25=slope^2<BR>\n" );
document.write( "2.5=slope <BR>\n" );
document.write( "top=2*2.5*l=5*l<BR>\n" );
document.write( "bottom=3*l <BR>\n" );
document.write( "5*l+3*l+6=38<BR>\n" );
document.write( "8*l=32<BR>\n" );
document.write( "l=4 <BR>\n" );
document.write( "V=hbl<BR>\n" );
document.write( "v=2*3*4=6*4=24 m^3\r<BR>\n" );
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document.write( "oh drat, I realized I made an error\r<BR>\n" );
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document.write( "volume of the prism standing up right would be area of base times the height<BR>\n" );
document.write( "in this case area of one of the triangular sides times the length\r<BR>\n" );
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document.write( "V should be 1/2 * base * height * length<BR>\n" );
document.write( "V= 1/2 * 3 * 2 * 4<BR>\n" );
document.write( "V= 1/2 * 6 * 4<BR>\n" );
document.write( "V= 1/2 * 24<BR>\n" );
document.write( "V=12 m^3 NOT 24 m^3 \r<BR>\n" );
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document.write( "family needed a tent that measures at least 10m^3\r<BR>\n" );
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document.write( "the tent still satisfies the requirements by 2 m^3<BR>\n" );
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