document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=384661>Question 384661</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ***I NEED THE STEPS TO SOLVE THIS PROBLEM SO THAT I CAN BETTER UNDERSTAND IT...PLEASE HELP*** \r<BR>\n" );
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document.write( "ANSWER: (a)2sqroot2 ft<BR>\n" );
document.write( "        (b) 2ft \r<BR>\n" );
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document.write( "PROBLEM: DIMENSIONS OF AN AQUARIUM <BR>\n" );
document.write( "An open-topped aquarium is to be constructed with 6ft-long sides and square ends. \r<BR>\n" );
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document.write( "(a) Find the height of the aquarium if the volume is to be 48ft^3.<BR>\n" );
document.write( "(b) Find the height if 44ft^2 of glass is to be used. \r<BR>\n" );
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document.write( "THANK YOU!!!!!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #272343 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=272343\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 6 foot long sides.<BR>\n" );
document.write( "square ends.\r<BR>\n" );
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document.write( "find height if volume is 48 cubic feet\r<BR>\n" );
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document.write( "Volume of rectangular prism is h*l*w (height * length * width)\r<BR>\n" );
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document.write( "length is 6 feet.\r<BR>\n" );
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document.write( "height and width (form the ends) are the same measure, call it s.\r<BR>\n" );
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document.write( "volume is therefore h*s^2 (height * area of the base)\r<BR>\n" );
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document.write( "formula for volume is v = h*s^2\r<BR>\n" );
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document.write( "height is 6 feet, so formula becomes v = 6*s^2\r<BR>\n" );
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document.write( "volume is 48 cubic feet, so formula becomes 48 = 6*s^2\r<BR>\n" );
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document.write( "divide both sides of equation by 6 to get 8 = s^2\r<BR>\n" );
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document.write( "take square root of both sides of equation to get s = sqrt(8).\r<BR>\n" );
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document.write( "length is 6<BR>\n" );
document.write( "width is sqrt(8)<BR>\n" );
document.write( "height is sqrt(8)\r<BR>\n" );
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document.write( "volume is l*w*h = 6*sqrt(8)*sqrt(8) = 6*8 = 48 cubic feet.\r<BR>\n" );
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document.write( "sqrt(8) = sqrt(2*2*2) = 2*sqrt(2)\r<BR>\n" );
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document.write( "(b) Find the height if 44 square feet of glass is to be used. \r<BR>\n" );
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document.write( "aquarium is open topped.\r<BR>\n" );
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document.write( "length is still 6 feet.\r<BR>\n" );
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document.write( "ends are still square.\r<BR>\n" );
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document.write( "aquarium is open on top.\r<BR>\n" );
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document.write( "it therefore has 2 sides (one on each end) and 3 sides along the length.\r<BR>\n" );
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document.write( "since the ends are still square, then the width equal the height and we can still call them s rather than w and h.\r<BR>\n" );
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document.write( "the area of each end is still s^2.\r<BR>\n" );
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document.write( "2 times the area of each end is therefore equal to 2*s^2.\r<BR>\n" );
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document.write( "the area of each side along the length will be s*l.\r<BR>\n" );
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document.write( "we have 3 of them.\r<BR>\n" );
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document.write( "the total area of the sides along the length is therefore 3*s*l\r<BR>\n" );
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document.write( "the side along the length on the top of the aquarium is open and so its area is not counted for total area of glass.\r<BR>\n" );
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document.write( "total area of glass is the area of the 2 ends plus the area along the length for 3 of the 4 sides along the length..\r<BR>\n" );
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document.write( "that equals 2*s^2 + 3*s*l which equals 44 square feet.\r<BR>\n" );
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document.write( "formula becomes 44 = 2*s^2 + 3*s*l\r<BR>\n" );
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document.write( "we know that l = 6, so we substitute 6 for l to get:\r<BR>\n" );
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document.write( "44 = 2*s^2 + 3*s*6 which becomes 44 = 2*s^2 + 18*s\r<BR>\n" );
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document.write( "subtract 44 from both sides of this equation to get the standard form of a quadratic equation of:\r<BR>\n" );
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document.write( "2*s^2 + 18*s -44 = 0\r<BR>\n" );
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document.write( "divide both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "s^2 + 9*s - 22 = 0\r<BR>\n" );
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document.write( "factor this equation to get:\r<BR>\n" );
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document.write( "(s+11) * (s-2) = 0\r<BR>\n" );
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document.write( "solve for s to get s = -11 or s = 2\r<BR>\n" );
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document.write( "s can't be negative, so s has to be equal to 2.\r<BR>\n" );
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document.write( "that's your answer.\r<BR>\n" );
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document.write( "total surface area = 2*4 + 3*2*6 = 8 + 36 = 44 square inches.\r<BR>\n" );
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document.write( "a picture of your aquarium that might help is shown here:\r<BR>\n" );
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document.write( " </SPAN>\n" );
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