document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=467363>Question 467363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you help me with this tough question?\r<BR>\n" );
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document.write( "\"An open box is to be constructed from 84 square inches of material. What should be the dimensions of the base if the height of the box is to be 2 inches? Surface Area: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=+x%5E2+%2B+4xh+ ALIGN=MIDDLE  ALT=\"S=+x%5E2+%2B+4xh+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #320700 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=320700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you are just looking for surface area, then the solution by Ankar is correct.<BR>\n" );
document.write( "you have 84 square inches of surface area and you are removing 16 square inches of surface area and you are left with 68 square inches of surface area.<BR>\n" );
document.write( "If you are assuming that the bottom of the box is square, than Ankar is correct again.<BR>\n" );
document.write( "You start with 84 square inches.<BR>\n" );
document.write( "You take the square root of 84 to get 9.16515139 inches on a side.<BR>\n" );
document.write( "That means your length is 9.16515139 inches and your Width is 9.16515139 inches.<BR>\n" );
document.write( "You remove a 2 inch by 2 inch section from each of the 4 corners.<BR>\n" );
document.write( "You then fold up the flaps on each end that are 2 inches in width. These will form the sides of the box that are 2 inches in height.<BR>\n" );
document.write( "You are left with a box that has a length of 5.16515139 inches and a width of 5.16515139 inches and a height of 2 inches.<BR>\n" );
document.write( "If you let L = length and W = width and H = height, then the formula for Volume (V) and for Surface Area (SA) will be:<BR>\n" );
document.write( "V = L * W * H<BR>\n" );
document.write( "SA =(L * W) + (2 * H * L) + (2 * H * W)<BR>\n" );
document.write( "This comes out to be:<BR>\n" );
document.write( "V = 5.16515139 * 5.16515139 * 2 = 53.35757776 cubic inches.<BR>\n" );
document.write( "SA = (5.16515139 * 5.16515139) + (2 * 2 * 5.16515139) + (2 * 2 * 5.16515139) = 68 square inches.<BR>\n" );
document.write( "If you recall what Ankar said, the Surface Area should be:<BR>\n" );
document.write( "84 square inches minus 16 square inches = 68 square inches.<BR>\n" );
document.write( "Since we also came up with a Surface Area of 68 square inches the long way, we're good.<BR>\n" );
document.write( "Since L = W because the bottom of the box is square, then we can change the formulas around just a little.<BR>\n" );
document.write( "We'll let S represent L and S represent W.<BR>\n" );
document.write( "S means Side.<BR>\n" );
document.write( "Your formula for Volume will change as follows:<BR>\n" );
document.write( "V = L * W * H becomes:<BR>\n" );
document.write( "V = S * S * H which becomes:<BR>\n" );
document.write( "V = S^2 * H.<BR>\n" );
document.write( "Your formula for Surface Area will change as follows:<BR>\n" );
document.write( "SA = (L * W) + (2 * H * L) + (2 * H * W) becomes:<BR>\n" );
document.write( "SA = (S * S) + (2 * H * S) + (2 * H * S) which becomes:<BR>\n" );
document.write( "SA = S^2 + (4 * H * S)<BR>\n" );
document.write( "Written without the multiplication signs, this becomes:<BR>\n" );
document.write( "SA = S^2 + 4HS<BR>\n" );
document.write( "If you replace H with h and you replace S with x, then you get:<BR>\n" );
document.write( "SA = x^2 + 4xh<BR>\n" );
document.write( "That's the formula you showed above, so we're doing the right thing.<BR>\n" );
document.write( "The formula you showed said that S = x^2 + 4xh.<BR>\n" );
document.write( "Replace SA with S and you have your formula.<BR>\n" );
document.write( "Ankar is right to assume the bottom of the box is square.<BR>\n" );
document.write( "It can only be square if all the sides are of equal length.<BR>\n" );
document.write( "It can only be square, if the formula for Surface Area is as shown.<BR>\n" );
document.write( "You were asked to find the value of x.<BR>\n" );
document.write( "The value of x is equal to 5.16515139<BR>\n" );
document.write( "This was the value of L and W and, subsequently S, that we found above..<BR>\n" );
document.write( "This can be rounded to whatever number of decimal places you require.<BR>\n" );
document.write( "If no rounding is required, then leave it as is.<BR>\n" );
document.write( "Round to:<BR>\n" );
document.write( "1 decimal place and x = 5.2<BR>\n" );
document.write( "2 decimal places and x = 5.17<BR>\n" );
document.write( "3 decimal places and x = 5.165<BR>\n" );
document.write( "4 decimal places and x = 5.1652<BR>\n" );
document.write( "etc. \r<BR>\n" );
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