document.write( "Question 1199465: A rectangle is 5 cm longer than its width. If its width is x cm and its area is 14 cm2. a)Form an equation in x. b)Solve the equation to find the value of x. (c) State the dimensions of the rectangle. \n" ); document.write( "

Algebra.Com's Answer #833352 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "The width is x cm.\r\n" );
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document.write( "The length is (x+5) cm.\r\n" );
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document.write( "The area of a rectangle is the product of the length by the width.\r\n" );
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document.write( "Therefore, the area equation for this problem is \r\n" );
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document.write( "    x*(x+5) = 14.     (1)\r\n" );
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document.write( "It can be transformed to the standard form quadratic equation\r\n" );
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document.write( "    x^2 + 5x = 14,\r\n" );
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document.write( "    x^2 + 5x - 14 = 0.     (2)\r\n" );
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document.write( "This quadratic equation can be solved in two ways: using the quadratic formula or by factoring.\r\n" );
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document.write( "The solution by factoring is extremely short and easy:  we factor left side as the product \r\n" );
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document.write( "    x^2 + 5x - 14 = (x+7)*(x-2).\r\n" );
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document.write( "Therefore, equation (2) takes the form\r\n" );
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document.write( "    (x+7)*(x-2) = 0.\r\n" );
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document.write( "It has two roots,  x= -7  and  x= 2.\r\n" );
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document.write( "In this problem, x is the width of a rectangle, so we are seeking for the positive value.\r\n" );
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document.write( "Therefore, we accept the positive value x= 2 and reject the negative value x= -7.\r\n" );
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document.write( "Thus the problem is just solved, and the answer is\r\n" );
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document.write( "    the width of the rectangle is  2 cm; its length is  2+5 = 7 cm.\r\n" );
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document.write( "CHECK.  2*7 = 14 cm^2, which coincides with the given area and confirms the answer.\r\n" );
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document.write( "In this way, the solution is complete.\r\n" );
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document.write( "If you want, you may use the quadratic formula, too.  It gives the roots\r\n" );
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document.write( "     =  =  = .\r\n" );
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document.write( "Thus   =  = 2;   =  = -7,  and we get the same roots.\r\n" );
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document.write( "Due to the same reason, we accept the positive root and reject the negative one.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The solution is complete in two ways with detailed explanations.\r
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\n" ); document.write( "\n" ); document.write( "On solving quadratic equations using the quadratic formula, see the lessons \r
\n" ); document.write( "\n" ); document.write( "    - Introduction into Quadratic Equations\r
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\n" ); document.write( "\n" ); document.write( "On solving quadratic equations by factoring see the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Solving quadratic equations without quadratic formula\r
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