document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80995>Question 80995</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the length of a rectangle is 5 cm more than 3 times its width. If the area of the rectangle is 95 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 #58103 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=58103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangle is 5 cm more than 3 times its width. If the area of the rectangle is 95 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 3 times width = 3x\r<BR>\n" );
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document.write( "5 cm more than 3 times its width = (3x + 5)cm\r<BR>\n" );
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document.write( "It is given that its length is 5cm more than 3 times its width\r<BR>\n" );
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document.write( "So length of the rectangle = (3x + 5) 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 95 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 = (3x + 5 ) * x\r<BR>\n" );
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document.write( "==> 95 = 3x * x + 5 * x\r<BR>\n" );
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document.write( "==> 95 = 3x^2 + 5x\r<BR>\n" );
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document.write( "Subtract 95 from both sides of the equation, then we will obtain a quadratic equation.\r<BR>\n" );
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document.write( "==> 95 - 95 = 3x^2 + 5x - 95\r<BR>\n" );
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document.write( "==> 0 = 3x^2 + 5x - 95\r<BR>\n" );
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document.write( "3x^2 + 5x - 95 = 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 = 3, b = 5 and c = -95\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+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A3%2A%28-95%29+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A3%2A%28-95%29+%29%29%2F%282%2A3%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+=+%28-5+%2B-+sqrt%28+25+%2B+1140+%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"x+=+%28-5+%2B-+sqrt%28+25+%2B+1140+%29%29%2F%286%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+=+%28-5+%2B-+34.13%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-5+%2B-+34.13%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "x = (-4 + 34.14)/6 or x = (-4 - 34.13 )/6\r<BR>\n" );
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document.write( "x = 30.14/6 or x = -38.13/6\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 = 5.023 cm\r<BR>\n" );
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document.write( "So width of the rectangle is 5.023 cm.\r<BR>\n" );
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document.write( "so width = 5.023 cm.\r<BR>\n" );
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document.write( "and length = 3x + 5 = 3 * (5.782) + 5 = 15.069 + 5 = 20.069 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 = 20.069 cm and\r<BR>\n" );
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document.write( "Width = 5.023 cm.\r<BR>\n" );
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document.write( "To check your answer, multiply length with breadth, then you will get 95 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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