document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1027377>Question 1027377</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cynthia Besch wants to buy a rug for a room that is 17 ft wide and 24 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 144 square feet of carpeting. What dimensions should the rug&#8203; have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #642572 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=642572\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the size of the room is 17 feet in width and 24 feet in length.\r<BR>\n" );
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document.write( "she wants to leave a uniform width of floor around the rug.\r<BR>\n" );
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document.write( "if we let that width be equal to the variable named x, then we get:\r<BR>\n" );
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document.write( "the dimensions of the room are 17 * 24.\r<BR>\n" );
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document.write( "the dimensions of the rug need to be (17-2x) * (24 - 2x).\r<BR>\n" );
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document.write( "this will leave a width of x surrounding each width of the rug and each length of the rug.\r<BR>\n" );
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document.write( "since the area of the rug is equal to 144, then we get:\r<BR>\n" );
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document.write( "(17-2x) * (24-2x) = 144.\r<BR>\n" );
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document.write( "simplify this equation by multiplying the expression on the left side using the distributive property of multiplication to get:\r<BR>\n" );
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document.write( "17*24 - 34x - 48x + 4x^2 = 144\r<BR>\n" );
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document.write( "simplify and combine like terms to get:\r<BR>\n" );
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document.write( "408 - 82x + 4x^2 = 144\r<BR>\n" );
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document.write( "rearrange the terms in descending order of degree to get:\r<BR>\n" );
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document.write( "4x^2 - 82x + 408 = 144\r<BR>\n" );
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document.write( "subtract 144 from both sides of the equation to get:\r<BR>\n" );
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document.write( "4x^2 - 82x + 264 = 0\r<BR>\n" );
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document.write( "take out the greatest common factor of 2 to get:\r<BR>\n" );
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document.write( "2 * (2x^2 - 41x + 132) = 0\r<BR>\n" );
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document.write( "factor the quadratic equation, using the quadratic formula, to get:\r<BR>\n" );
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document.write( "x = 4 or x = 16.5\r<BR>\n" );
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document.write( "our original equation is (17-2x) * (24-2x) = 144.\r<BR>\n" );
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document.write( "when x = 16.5, the dimensions become 0 which is not valid, so x = 16.5 is an extraneous solution and is discarded.\r<BR>\n" );
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document.write( "when x = 4, the dimensions becomes (17-8) * (24-8) = 144.\r<BR>\n" );
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document.write( "this results in 9 * 16 = 144 which results in 144 = 144 which confirms this solution is good.\r<BR>\n" );
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document.write( "we have x = 4.\r<BR>\n" );
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document.write( "the rug will be 9 by 16 and will have a border of 4 feet surrounding each length of the rug and each width of the rug.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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