document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204421>Question 1204421</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cynthia Besch wants to buy a rug for a room that is  27ft wide and  35ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 609 square feet of carpeting. What dimensions should the rug​ have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840651 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=840651\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "A question like this has been asked before.\r<BR>\n" );
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document.write( "Review this link to see an example how to solve.<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.1197474.html\">https://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.1197474.html</a>\r<BR>\n" );
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document.write( "If you are still stuck, then read on.\r<BR>\n" );
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document.write( "Draw out a diagram as indicated in the link above.\r<BR>\n" );
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document.write( "There will be a large rectangle that is 27 feet by 35 feet. <BR>\n" );
document.write( "This represents the dimensions of the room.\r<BR>\n" );
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document.write( "Inside that larger rectangle will be a smaller rectangle with dimensions (27-2x) feet by (35-2x) feet.<BR>\n" );
document.write( "x represents the width of the uniform strip. <BR>\n" );
document.write( "This is the buffer gap between the edge of the rug to the edge of the wall.\r<BR>\n" );
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document.write( "The area of the smaller rectangle is (27-2x)(35-2x).<BR>\n" );
document.write( "Set this equal to 609 because this is the amount of carpet she can buy.\r<BR>\n" );
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document.write( "(27-2x)(35-2x) = 609<BR>\n" );
document.write( "27(35-2x)-2x(35-2x) = 609<BR>\n" );
document.write( "945-54x-70x+4x^2 = 609<BR>\n" );
document.write( "945-54x-70x+4x^2 - 609 = 0<BR>\n" );
document.write( "4x^2 - 124x + 336 = 0<BR>\n" );
document.write( "4(x^2 - 31x + 84) = 0<BR>\n" );
document.write( "x^2 - 31x + 84 = 0\r<BR>\n" );
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document.write( "We could factor, but I think the quadratic formula is the most efficient pathway. <BR>\n" );
document.write( "This is because we don't have to worry about guess-and-check.\r<BR>\n" );
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document.write( "Plug a = 1, b = -31, c = 84 into the quadratic formula below.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-31%29%2B-sqrt%28%28-31%29%5E2-4%281%29%2884%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-31%29%2B-sqrt%28%28-31%29%5E2-4%281%29%2884%29%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2856%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2856%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%286%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+28 ALIGN=MIDDLE  ALT=\"x+=+28\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If x = 28, then 27-2x = 27-2*28 = -29, which is not valid. <BR>\n" );
document.write( "The side length must be positive.\r<BR>\n" );
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document.write( "If x = 3, then, <BR>\n" );
document.write( "27-2x = 27-2*3 = 21<BR>\n" );
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document.write( "35-2x = 35-2*3 = 29<BR>\n" );
document.write( "Both results are positive. <BR>\n" );
document.write( "Therefore x = 3 is valid and practical.<BR>\n" );
document.write( "A gap of 3 feet produces a rug that is 21 feet by 29 feet.\r<BR>\n" );
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document.write( "As a check, 21*29 = 609, and we have confirmed the answer is correct.\r<BR>\n" );
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document.write( "<font size=4>Answer:</font> The rug should be 21 feet by 29 feet.<BR>\n" );
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