document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197474>Question 1197474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 31 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy  253 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 #830761 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=830761\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = width of the uniform strip (i.e. the gap between the rug edge and the wall)\r<BR>\n" );
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document.write( "Diagram<BR>\n" );
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document.write( "The larger rectangle is 19 by 31<BR>\n" );
document.write( "The smaller rectangle inside is (19-2x) by (31-2x)\r<BR>\n" );
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document.write( "The smaller rectangle area is 253 sq ft<BR>\n" );
document.write( "length*width = area<BR>\n" );
document.write( "(19-2x)*(31-2x) = 253<BR>\n" );
document.write( "19*(31-2x) - 2x*(31-2x) = 253<BR>\n" );
document.write( "589 - 38x - 62x + 4x^2 = 253<BR>\n" );
document.write( "589 - 100x + 4x^2 = 253<BR>\n" );
document.write( "589 - 100x + 4x^2 - 253 = 0<BR>\n" );
document.write( "4x^2 - 100x + 336 = 0\r<BR>\n" );
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document.write( "Compare this to ax^2+bx+c = 0<BR>\n" );
document.write( "a = 4<BR>\n" );
document.write( "b = -100<BR>\n" );
document.write( "c = 336\r<BR>\n" );
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document.write( "Use the quadratic formula to isolate x.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+21 ALIGN=MIDDLE  ALT=\"x+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If x = 21, then 19-2x = 19-2*21 = 19-42 = -23 which isn't possible. <BR>\n" );
document.write( "A negative length or width makes no sense.<BR>\n" );
document.write( "We'll ignore x = 21.\r<BR>\n" );
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document.write( "The only practical solution is x = 4.<BR>\n" );
document.write( "If x = 4, then 19-2x = 19-2*4 = 19-8 = 11<BR>\n" );
document.write( "If x = 4, then 31-2x = 31-2*4 = 31-8 = 23<BR>\n" );
document.write( "Both results are positive.<BR>\n" );
document.write( "The carpet is 11 by 23 to get an area of 11*23 = 253 sq ft. This verifies the answer.\r<BR>\n" );
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document.write( "Answer: <font color=red>11 ft by 23 ft</font><BR>\n" );
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