document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189165>Question 1189165</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear Colleagues\r<BR>\n" );
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document.write( "I have the following question to find a solution to:<BR>\n" );
document.write( "The length of a rectangle exceeds its breadth by 4 centimetres.  If the length were halved and the breadth increased by 5 centimetres, the area would be decreased by 35 square centimetres.  Find the length of the rectangle.\r<BR>\n" );
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document.write( "I do not know if I can draw in this website, but whilst trying to find the solutions, I drew 2 rectangles: the one on the left had the dimensions (x)(x+4) for width and length respectively, the one on the right had dimensions ((x+4)/2)(x+5) for length and width respectively.<BR>\n" );
document.write( "The question then reads - for me - [((x+4)/2)(x+5)] - 35 = x(x+4)<BR>\n" );
document.write( "Multiplying the left hand by 2 to clear the fraction, we get<BR>\n" );
document.write( "[(x+4)(2x+10)]-35 = x(x+4)<BR>\n" );
document.write( "and after multiplying out we get<BR>\n" );
document.write( "[2x^2+10x+8x+40]-35 = x^2+4x<BR>\n" );
document.write( "Collecting like terms gives us<BR>\n" );
document.write( "2x^2+18x+5 = x^2+4x<BR>\n" );
document.write( "which simplifies to<BR>\n" );
document.write( "x^2+14x+5=0<BR>\n" );
document.write( "We cannot factorise, so using the quadratic formula we get<BR>\n" );
document.write( "a = 1, b= 14, c = 5<BR>\n" );
document.write( "and putting all of this into the formula we get\r<BR>\n" );
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document.write( "x = (-b+/- sqrt of b^2-4ac)/2<BR>\n" );
document.write( "which gives<BR>\n" );
document.write( "x = (-14 +/- sqrt (14)^2-(4)(1)(5))/2\r<BR>\n" );
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document.write( "which gives us, finally, x = (-14 +/-13.23)/2\r<BR>\n" );
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document.write( "I am assuming that we need a real number for the length of the side of the rectangle, so do not wish to get into imaginary numbers...<BR>\n" );
document.write( "Where have I gone wrong? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820426 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=820426\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "Dear Colleagues\r\n" );
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document.write( "I have the following question to find a solution to:\r\n" );
document.write( "The length of a rectangle exceeds its breadth by 4 centimetres.  If the length were halved and the breadth \r\n" );
document.write( "increased by 5 centimetres, the area would be decreased by 35 square centimetres.  Find the length of the rectangle.\r\n" );
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document.write( "I do not know if I can draw in this website, but whilst trying to find the solutions, I drew 2 rectangles: \r\n" );
document.write( "the one on the left had the dimensions (x)(x+4) for width and length respectively, \r\n" );
document.write( "the one on the right had dimensions ((x+4)/2)(x+5) for length and width respectively.\r\n" );
document.write( "The question then reads - for me - [((x+4)/2)(x+5)] - 35 = x(x+4)   <<<---===\r\n" );
document.write( "Multiplying the left hand by 2 to clear the fraction, we get\r\n" );
document.write( "[(x+4)(2x+10)]-35 = x(x+4)\r\n" );
document.write( "and after multiplying out we get\r\n" );
document.write( "[2x^2+10x+8x+40]-35 = x^2+4x\r\n" );
document.write( "Collecting like terms gives us\r\n" );
document.write( "2x^2+18x+5 = x^2+4x\r\n" );
document.write( "which simplifies to\r\n" );
document.write( "x^2+14x+5=0\r\n" );
document.write( "We cannot factorise, so using the quadratic formula we get\r\n" );
document.write( "a = 1, b= 14, c = 5\r\n" );
document.write( "and putting all of this into the formula we get\r\n" );
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document.write( "x = (-b+/- sqrt of b^2-4ac)/2\r\n" );
document.write( "which gives\r\n" );
document.write( "x = (-14 +/- sqrt (14)^2-(4)(1)(5))/2\r\n" );
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document.write( "which gives us, finally, x = (-14 +/-13.23)/2\r\n" );
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document.write( "I am assuming that we need a real number for the length of the side of the rectangle, \r\n" );
document.write( "so do not wish to get into imaginary numbers...\r\n" );
document.write( "Where have I gone wrong?\r\n" );
document.write( "</PRE>~~~~~~~~~~~~~~~~\r<BR>\n" );
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document.write( "Your error is in the line, which I marked by &nbsp;&nbsp;&nbsp;&nbsp;<<<---=== .\r<BR>\n" );
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document.write( "The correct form of this equation is\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[((x+4)/2)(x+5)] + 35 = x(x+4).\r<BR>\n" );
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document.write( "I did not develop my solution farther, since I see that your technique is enough<BR>\n" );
document.write( "in order for you complete it on your own.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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