document.write( "Question 1102530: the perimeter of a rectangular garden is 420 cm . If its length is increased by 20% and breadth is decreased by 40 % , we get the same perimeter. then the length and breadth of the new formed rectangular garden , respectively are \n" ); document.write( "

Algebra.Com's Answer #717291 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "the perimeter of a rectangular garden is 420 cm . If its length is increased by 20% and breadth is decreased by 40 % ,
\n" ); document.write( "we get the same perimeter. then the length and breadth of the new formed rectangular garden , respectively are
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\n" ); document.write( "        The solution by @josgarithmetic is not correct. The correct solution is placed below.
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document.write( "Let L be the length and W be the width of the rectangular garden (the original dimensions).\r\n" );
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document.write( "Then the first equation is\r\n" );
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document.write( "2L + 2W = 420,   or  L + W = 210.\r\n" );
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document.write( "The second equation is \r\n" );
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document.write( "2*(1.2L) + 2*(0.6W) = 420,   or  1.2L + 0.6W = 210.\r\n" );
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document.write( "So, you have the system of 2 equations in 2 unknowns\r\n" );
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document.write( "   L +    W = 210,    (1)\r\n" );
document.write( "1.2L + 0.6W = 210.    (2)\r\n" );
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document.write( "From eq(1) express W = 210-L  and substitute it into eq(2). You will get\r\n" );
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document.write( "1.2L + 0.6*(210-L) = 210,\r\n" );
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document.write( "1.2L + 0.6*210 - 0.6L = 210  ====>  0.6L = 210 - 0.6*210 = 0.4*210  ====>  L =  = 140.\r\n" );
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document.write( "Thus we just found L = 140 cm.\r\n" );
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document.write( "Then W = 210 - L = 210 - 140 = 70 cm.\r\n" );
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document.write( "The original length was 140 cm.  The original width was 70 cm.\r\n" );
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document.write( "Check.   140 + 70 + 140 + 70 = 420.    ! Correct !\r\n" );
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document.write( "         2*140*1.2 + 2*70*0.6 = 420.   ! Correct !\r\n" );
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document.write( "The new dimensions are:  1.2*L = 1.2*140 = 168 cm (length)  and  0.6*W = 0.6*70 = 42 cm.\r\n" );
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document.write( "Answer.  The new dimensions are:  168 cm (length)  and  42 cm (width).\r\n" );
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