document.write( "Question 1112707: Cynthia Besch wants to buy a rug for a room that is \r
\n" ); document.write( "\n" ); document.write( "8 ft wide and \r
\n" ); document.write( "\n" ); document.write( "19 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy \r
\n" ); document.write( "\n" ); document.write( "102 square feet of carpeting. What dimensions should the rug have? \n" ); document.write( "

Algebra.Com's Answer #727740 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Let \"x\" be the uniform width of the strip. \r\n" );
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document.write( "Then the dimensions of the rug are (8-2x) and (19-2x). \r\n" );
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document.write( "Thus the area of the rug is (8-2x)*(19-2x).\r\n" );
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document.write( "According to the condition, it must be equal to 102.  It gives you an equation\r\n" );
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document.write( "(8-2x)*(19-2x) = 102\r\n" );
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document.write( " = 102\r\n" );
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document.write( " = 0\r\n" );
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document.write( " = 0\r\n" );
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document.write( "The discriminant   d =  = 529.\r\n" );
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document.write( " =  = .\r\n" );
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document.write( "There are two roots.\r\n" );
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document.write( " = /4 = 12.5  is, obviously, too big (more than the wide of the room) and, therefore, does not work as the solution to the problem.\r\n" );
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document.write( " =  = 1  perfectly suits as the solution.\r\n" );
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document.write( "So, the wide of the strip is 1 ft and the dimensions of the rug are  8 - 2*1 = 6 ft wide  and  19 - 2*1 = 17 ft long.\r\n" );
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document.write( "Check.  (8-2*1)*(19-2*1) = 6*17 = 102.\r\n" );
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document.write( "Answer.  The rug should be 6 by 17 feets.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is classic algebraic solution.\r
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\n" ); document.write( "\n" ); document.write( "You can solve the problem MENTALLY, too.\r
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document.write( "The difference between the room dimensions is 19-8 = 11 ft.\r\n" );
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document.write( "Since the strip is of uniform width, the dimensions of the rug must have the same difference of 11 ft.\r\n" );
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document.write( "So, you will solve the problem, if you find the decomposition of the number of 102 into the product of two factors,\r\n" );
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document.write( "whose difference is 11.\r\n" );
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document.write( "There are, actually, only one such a possibility 102 = 6*17, which you can find in a minute (if not in 3 seconds).\r\n" );
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document.write( "At this point your mental solution is completed.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thank you for your patience reading my solution from the beginning to the end.\r
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\n" ); document.write( "\n" ); document.write( "You can find many other similar solved problems in the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Problems on the area and the dimensions of a rectangle surrounded by a strip\r
\n" ); document.write( "\n" ); document.write( "    - Problems on a circular pool and a walkway around it\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic
\n" ); document.write( "\"Dimensions and the area of rectangles and circles and their elements\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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\n" ); document.write( "\n" ); document.write( "The tutor @MathTherapy just explained to you that the original solution by @josgarithmetic was wrong.\r
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\n" ); document.write( "\n" ); document.write( "If you are permanent visitor of this forum, you, probably, just know, that @josgarithmetic is a person who solve incorrectly
\n" ); document.write( "every second or every third problem here in the forum.\r
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\n" ); document.write( "\n" ); document.write( "If you are a newcomer to the forum, I simply inform you about it.\r
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\n" ); document.write( "\n" ); document.write( "Therefore, when you get the solution from him, for your safety, do not hurry to accept it: there is high probability it is WRONG.\r
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\n" ); document.write( "\n" ); document.write( "Wait for reaction/solutions from other tutors.\r
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