document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80865>Question 80865</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I'd greatly appreciate help with this word problem: The length of a rectangle is 4 cm more than 2 times its width.  If the area of the rectangle is 90 cm^2, find the dimensions of the rectangle to the nearest thousandth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58012 by </B><A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><B>praseenakos@yahoo.com(507)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><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=praseenakos@yahoo.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=58012\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> QUESTION:\r<BR>\n" );
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document.write( "The length of a rectangle is 4 cm more than 2 times its width.  If the area of the rectangle is 90 cm^2, find the dimensions of the rectangle to the nearest thousandth.\r<BR>\n" );
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document.write( "ANSWER:\r<BR>\n" );
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document.write( "Assume that width of the rectangle is  'x' cm.\r<BR>\n" );
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document.write( "Then two times width = 2x\r<BR>\n" );
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document.write( "4 cm more than 2 times its width = (2x + 4)cm\r<BR>\n" );
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document.write( "It is given that its length is  4 cm more than 2 times its width\r<BR>\n" );
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document.write( "So length of the rectangle = (2x + 4 ) cm.\r<BR>\n" );
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document.write( "Area of a rectangle is given by the formula, A = length * width\r<BR>\n" );
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document.write( "Here  area is given that 90 cm^2\r<BR>\n" );
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document.write( "So we can write it as,\r<BR>\n" );
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document.write( "90 = (2x + 4 ) * x\r<BR>\n" );
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document.write( "==> 90 = 2x * x  + 4 * x\r<BR>\n" );
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document.write( "==> 90 = 2x^2 + 4x\r<BR>\n" );
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document.write( "Subtract 90 from both sides of the equation, then we will obtain a quadratic equation.\r<BR>\n" );
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document.write( "==> 90 - 90 = 2x^2 + 4x - 90\r<BR>\n" );
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document.write( "==> 0 = 2x^2 + 4x - 90\r<BR>\n" );
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document.write( "2x^2 + 4x - 90 = 0\r<BR>\n" );
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document.write( "We can solve this equation using quadratic formula.\r<BR>\n" );
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document.write( "standard form of a quadratic equation is,\r<BR>\n" );
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document.write( "ax^2 + bx + c = 0 ---------------(2)\r<BR>\n" );
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document.write( "By quadratic formula, the solution is given by,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Comparing (1) and (2) we have,\r<BR>\n" );
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document.write( "a = 2, b = 4 and c = -90\r<BR>\n" );
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document.write( "so the solution is,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A2%2A%28-90%29+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A2%2A%28-90%29+%29%29%2F%282%2A2%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+=+%28-4+%2B-+27.129%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+27.129%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "x = (-4 + 27.129)/4   or x = (-4 - 27.129 )/4\r<BR>\n" );
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document.write( "x = 23.129/4     or x = -41.129/4\r<BR>\n" );
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document.write( "( since negative values are not admisible here)\r<BR>\n" );
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document.write( "==> x = 5.782 cm\r<BR>\n" );
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document.write( "So width of the rectangle is 5.782  cm. \r<BR>\n" );
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document.write( "so width = 5.782 cm.\r<BR>\n" );
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document.write( "and length = 2x + 4 = 2 * (5.782) + 4 = 11. 564 + 4 = 15.564 cm\r<BR>\n" );
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document.write( "So the dimenstions of the given rectangle:\r<BR>\n" );
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document.write( "length = 15. 564 cm   and\r<BR>\n" );
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document.write( "Width  = 5.782 cm.\r<BR>\n" );
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document.write( "To check your answer, multiply lenth with breadth, then you will get 90 approximately.\r<BR>\n" );
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document.write( "Hope you  understood.\r<BR>\n" );
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document.write( "Regards.\r<BR>\n" );
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document.write( "Praseena.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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