document.write( "Question 1169995: The length of a rectangular field is 15 meters more than its width. If the area is less than 100, what could be the possible dimensions of the field? \n" ); document.write( "

Algebra.Com's Answer #794862 by ikleyn(52949) $\"\"$ $\"About$

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document.write( "Let x be the smaller dimension, in meters (the width).\r\n" );
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document.write( "Then the larger dimension (the length) is (x+15) meters, according to the condition.\r\n" );
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document.write( "They want you determine x in a way to satisfy inequality\r\n" );
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document.write( "    x*(x+15) < 100.\r\n" );
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document.write( "It is equivalent to \r\n" );
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document.write( "    x^2 + 15x - 100 < 0,\r\n" );
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document.write( "or, in factored form\r\n" );
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document.write( "    (x+20)*(x-5) < 0.\r\n" );
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document.write( "The solution to this inequality is the set\r\n" );
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document.write( "    -20 < x < 5.\r\n" );
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document.write( "But due to the meaning of x, the dimension x must be positive.\r\n" );
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document.write( "Therefore, the final solution is the set of real numbers  0 < x < 5 meters.\r\n" );
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document.write( "ANSWER.  The width must be shorter than 5 meters;  the length is 15 meters greater than the width.\r\n" );
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