document.write( "Question 1202194: The area of a rectangle is 45m^2, and the length of the rectangle is 1m more than twice the width. Find the dimensions of the rectangle.
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Algebra.Com's Answer #836864 by ikleyn(52777)\"\" \"About 
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\n" ); document.write( "The area of a rectangle is 45m^2, and the length of the rectangle is 1m more
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\n" ); document.write( "\n" ); document.write( "        I will show you a simple way to solve the problem  MENTALLY.\r
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document.write( "Let W be the width, in meters; then the length is (2W+1) meters.\r\n" );
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document.write( "The area equation is\r\n" );
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document.write( "    W*(2W+1) = 45.\r\n" );
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document.write( "Multiply both sides by 2.  You will get\r\n" );
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document.write( "    2W*(2W+1) = 90.    (1)\r\n" );
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document.write( "So, the product of two numbers, (2W) and (2W+1), is 90, and the numbers differ by 1.\r\n" );
document.write( "At this point, you can easily guess the solution: it is 2W = 9  and  W = 9/2 = 4.5.\r\n" );
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document.write( "Next, left side of equation (1) is monotonically increasing function for positive W.\r\n" );
document.write( "It means that equation (1) has a UNIQUE solution in positive numbers, which we just found.\r\n" );
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document.write( "ANSWER. The problem has a unique solution: the width is 4.5 m; the length is 2*4.5+1 = 10 m.\r\n" );
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\n" ); document.write( "\n" ); document.write( "My reasoning in this solution is mathematically and logically absolutely strict,
\n" ); document.write( "although it includes an element of guessing; but this guessing is supported
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\n" ); document.write( "\n" ); document.write( "It is much easier than to factor a quadratic equation on the way
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\n" ); document.write( "\n" ); document.write( "Such approach works for many other similar problems.\r
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\n" ); document.write( "\n" ); document.write( "        About factoring, I always repeat my standard joke: \r
\n" ); document.write( "\n" ); document.write( "        it works especially good, when you know an answer in advance.\r
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