document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134511>Question 134511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of a pool is 3 times its width, and the pool is surrounded by a grass walk 4 feet wide.  If the total area enclosed by the walk (of uniform width) is 684 square feet, find the dimensions of the pool.\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 #98406 by </B><A HREF=/tutors/aboutme.mpl?userid=nycsharkman><B>nycsharkman(136)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nycsharkman><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=98406\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The length of a pool is 3 times its width, and the pool is surrounded by a grass walk 4 feet wide.  If the total area enclosed by the walk (of uniform width) is 684 square feet, find the dimensions of the pool.\r<BR>\n" );
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document.write( "This is quadratic equation word problem using a geometric figure...our swimming pool.\r<BR>\n" );
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document.write( "Information Given:\r<BR>\n" );
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document.write( "width = x...x is the unknown.\r<BR>\n" );
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document.write( "length = 3 times x or 3x.\r<BR>\n" );
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document.write( "Area = 684ft^2...We use a square because area is measured in SQUARE UNITS.\r<BR>\n" );
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document.write( "Grass walk = 4 feet wide\r<BR>\n" );
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document.write( "We know that if the grass walk surrounds the pool, it must be 4 feet wide all AROUND the pool.  Make sense?\r<BR>\n" );
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document.write( "Here is the equation:\r<BR>\n" );
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document.write( "(3x + 8) times (x + 8) = 684\r<BR>\n" );
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document.write( "We use the FOIL method on the left side to get:\r<BR>\n" );
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document.write( "3x^2 + 24x + 8x + 64, which then becomes:\r<BR>\n" );
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document.write( "3x^2 + 32x + 64\r<BR>\n" );
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document.write( "We equate 3x^2 + 32x + 64 to the given area and we get:\r<BR>\n" );
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document.write( "3x^2 + 32x + 64 = 684\r<BR>\n" );
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document.write( "Subtract 684 from BOTH sides and we are left with:\r<BR>\n" );
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document.write( "3x^2 + 32x + 64 - 684 = 0\r<BR>\n" );
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document.write( "3x^2 + 32x -620 = 0\r<BR>\n" );
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document.write( "Factor the left side using groups.\r<BR>\n" );
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document.write( "3x^2 + 62x - 30x - 620 = 0\r<BR>\n" );
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document.write( "(3x^2 + 62x) = Group A\r<BR>\n" );
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document.write( "(- 30x - 620) = Group B\r<BR>\n" );
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document.write( "Factor each group separately.\r<BR>\n" );
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document.write( "Group A becomes x(3x + 62).\r<BR>\n" );
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document.write( "Group B becomes -10(3x + 32)\r<BR>\n" );
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document.write( "We now have this equation:\r<BR>\n" );
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document.write( "(x - 10)(3x + 62) = 0\r<BR>\n" );
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document.write( "Set each factor to 0 and solve for x.\r<BR>\n" );
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document.write( "x - 10 = 0\r<BR>\n" );
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document.write( "x = 10\r<BR>\n" );
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document.write( "===========\r<BR>\n" );
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document.write( "3x + 62 = 0\r<BR>\n" );
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document.write( "3x = -62\r<BR>\n" );
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document.write( "x = -62/3....This value for x is REJECTED because we are looking for the dimensions of the pool.  Dimensions are distances and DISTANCE CANNOT be negative.  Is this clear?\r<BR>\n" );
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document.write( "We use x = 10 to find our dimensions.\r<BR>\n" );
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document.write( "As I said above:\r<BR>\n" );
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document.write( "width = x\r<BR>\n" );
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document.write( "length = 3 times x or 3x\r<BR>\n" );
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document.write( "I just found that x = 10, right?\r<BR>\n" );
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document.write( "Then our width is 10 feet and the length is 3x = 3(10) = 30 feet.\r<BR>\n" );
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document.write( "Width = 10 feet<BR>\n" );
document.write( "Length = 30 feet\r<BR>\n" );
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document.write( "Got it?\r<BR>\n" );
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document.write( " </SPAN>\n" );
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