Algebra.Com's Answer #825519 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( "Doris walks 89 feet diagonally across a rectangular field.
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document.write( "She then returns to her starting position along the outside of the field.
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document.write( "The total distance she walks is 208 feet. What are the dimensions of the field?
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document.write( "I would assume you could use the Pythagorean theorem for this,
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document.write( "but when I tried I did not get an answer that added up to 208.
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document.write( "Please explain step-by-step so I can understand how to solve the problem! Thanks.
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document.write( "Let x and y be the dimensions of the rectangle.\r\n" );
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document.write( "Then from the given part of the problem, we have these two independent equations\r\n" );
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document.write( "  =  (1) (the diagonal)\r\n" );
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document.write( "  + x + y = 208 (2) (the total distance)\r\n" );
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document.write( "In the second equation, replace by 89, based on equation (1).\r\n" );
document.write( "Keep first equation as is. Then you get this simplified system\r\n" );
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document.write( " = (1') \r\n" );
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document.write( " 89 + x + y = 208 (2') \r\n" );
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document.write( "You can simplify it further \r\n" );
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document.write( " = (1'') \r\n" );
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document.write( " x + y = 119 (2'') (because 208-89 = 119).\r\n" );
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document.write( "Next step square equation (2''); keep equation (1'') as is\r\n" );
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document.write( " = (3)\r\n" );
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document.write( "  =  (4)\r\n" );
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document.write( "Now subtract equation (3) from equation (4). You will get\r\n" );
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document.write( " 2xy = - = 6240\r\n" );
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document.write( "or\r\n" );
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document.write( " xy = 3120. (5)\r\n" );
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document.write( "Now combine equations (2'') and (5) into one system\r\n" );
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document.write( " x + y = 119 (6)\r\n" );
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document.write( " xy = 3120. (7)\r\n" );
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document.write( "It admits straightforward solution. From equation (6), express x = 119-y\r\n" );
document.write( "and substitute it into equation (7). You will get a quadratic equation\r\n" );
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document.write( " (119-y)*y = 3120,\r\n" );
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document.write( "or\r\n" );
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document.write( " y^2 - 119y + 3120 = 0.\r\n" );
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document.write( "You can solve it by factoring or by applying the quadratic formula.\r\n" );
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document.write( "In any case, the factoring is\r\n" );
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document.write( " (x-80)*(x-39) = 0\r\n" );
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document.write( "and the roots are 80 and 39.\r\n" );
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document.write( "These roots give the dimensions of the rectangle.\r\n" );
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document.write( "ANSWER. The dimensions of the rectangle are 80 feet by 39 feet.\r\n" );
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document.write( "Solved.\r
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document.write( "You may check my solution/answer by substituting the found dimensions into equations (1) and (2).\r
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document.write( "From my post, you need to learn these major lessons:\r
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document.write( " - (a) how to reduce this word problem to equations (1) and (2).\r
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document.write( " - (b) how to reduce this system (1), (2) to system (6), (7).\r
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document.write( " - (c) how to solve system (6), (7).\r
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document.write( "If you will learn it, then my and your job won't go to waste.\r
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