document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=493890>Question 493890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have this Geometry/Algebra word problem that I'm not even sure is solvable, I and my entire family have racked our brains over it for hours. Here it goes.\r<BR>\n" );
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document.write( "a) Define variables<BR>\n" );
document.write( "b) Give and equation<BR>\n" );
document.write( "c) Give solution\r<BR>\n" );
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document.write( "A rectangle is constructed. The length of this rectangle is double the width. Then a new rectangle is made by increasing each side by 3 meters. The perimeter of the new rectangle is 2 meters greater than 4 times the length of the old rectangle. Find the dimensions of the original rectangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #335488 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=335488\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangle is constructed. The length of this rectangle is double the width. Then a new rectangle is made by increasing each side by 3 meters. The perimeter of the new rectangle is 2 meters greater than 4 times the length of the old rectangle. Find the dimensions of the original rectangle.\r<BR>\n" );
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document.write( "first rectangle:\r<BR>\n" );
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document.write( "L = 2x<BR>\n" );
document.write( "W = x\r<BR>\n" );
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document.write( "second rectangle:\r<BR>\n" );
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document.write( "L = 2x + 3<BR>\n" );
document.write( "W = x + 3<BR>\n" );
document.write( "P = 2(2x+3) + 2(x+3) = 4x+6+2x+6 = 6x+12\r<BR>\n" );
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document.write( "L = length<BR>\n" );
document.write( "W = width<BR>\n" );
document.write( "P = perimeter\r<BR>\n" );
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document.write( "P (second rectangle) = 4 * (Length of first rectangle) + 2\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "6x+12 = 4(2x) + 2 which becomes:<BR>\n" );
document.write( "6x+12 = 8x+2<BR>\n" );
document.write( "subtract 6x from both sides of the equation to get:<BR>\n" );
document.write( "12 = 2x + 2<BR>\n" );
document.write( "subtract 2 from both sides of the equation to get:<BR>\n" );
document.write( "10 = 2x<BR>\n" );
document.write( "divide both sides of the equation by 2 to get:<BR>\n" );
document.write( "x = 5\r<BR>\n" );
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document.write( "when x = 5:\r<BR>\n" );
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document.write( "length of first rectangle becomes 2x = 10<BR>\n" );
document.write( "width of first rectangle becomes x = 5\r<BR>\n" );
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document.write( "length of second rectangle becomes 2x + 3 = 13<BR>\n" );
document.write( "width of second rectangle becomes x + 3 = 8\r<BR>\n" );
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document.write( "perimeter of second rectangle becomes 2*13 + 2*8 = 26+16 = 42\r<BR>\n" );
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document.write( "4 times length of first rectangle plus 2 becomes 4*10 + 2 = 42\r<BR>\n" );
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document.write( "requirements of problem are satisfied.\r<BR>\n" );
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document.write( "answer is that the dimensions of the original rectangle are:\r<BR>\n" );
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document.write( "length = 10<BR>\n" );
document.write( "width = 5\r<BR>\n" );
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document.write( " </SPAN>\n" );
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