document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205671>Question 1205671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made (see the accompanying figure). If the cardboard is l = 16 in. long and w = 9 in. wide, find the dimensions of the resulting box if it is to have a total surface area of 128 in.2<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842630 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=842630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the total surface of the rectangular piece of cardboard, before cutting, is equal to 16 * 9 = 144 square inches.\r<BR>\n" );
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document.write( "if you remove a square of x inches on a side from each corner of the box, the remaining surface area will be 16 * 9 - 4 * x^2 = 144 - 4 * x^2\r<BR>\n" );
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document.write( "if the remaining surface area is 128 square inches, then your formula becomes 144 - 4 * x^2 = 128.\r<BR>\n" );
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document.write( "add 4 * x^2 to both sides and subtract 128 from both sides of the equation to get 144 - 128 = 4 * x^2 which simplifies to 16 = 4 * x^2 which simplifies further to 4 = x^2.\r<BR>\n" );
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document.write( "solve for x to get x = 2.\r<BR>\n" );
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document.write( "the length will be 16 minus 2 * 2 = 12<BR>\n" );
document.write( "the width will be 9 minus 2 * 2 = 5<BR>\n" );
document.write( "the height will be 2.\r<BR>\n" );
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document.write( "the area of the bottom of the box will be 12 * 5 = 60<BR>\n" );
document.write( "the area of the 2 vertical sides along the length will be 12 * 2 = 24 each for a total area of 48.<BR>\n" );
document.write( "the area of the 2 vertical sides along the width will be 5 * 2 = 10 each for a total area of 20.\r<BR>\n" );
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document.write( "the total surface area of the box will be 60 + 48 + 20 = 128 square inches.\r<BR>\n" );
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