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 #820429 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=820429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i did it my way and i think i got the right answer.<BR>\n" );
document.write( "see my worksheet below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/122904.jpg\" >\r<BR>\n" );
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document.write( "looking at the way you did it, i think i know where you went wrong.\r<BR>\n" );
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document.write( "here's my worksheets about the way you did it.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/122905.jpg\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/122906.jpg\" >\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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