document.write( "Question 752457: The area of a rectangle remains unchanged when it is made 2cm shorter and 2cm wider or when it is made 8cm longer and 4cm narrower. what is its area, in square cm. \n" ); document.write( "

Algebra.Com's Answer #457739 by Edwin McCravy(20055) $\"\"$ $\"About$

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The area of a rectangle remains unchanged when it is made 2cm shorter and 2cm wider or when it is made 8cm longer and 4cm narrower. what is its area, in square cm.
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document.write( "LW = (L-2)(W+2) = (L+8)(W-4)\r\n" );
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document.write( "LW = LW+2L-2W-4 = LW-4L+8W-32\r\n" );
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document.write( "Subtract LW from all three\r\n" );
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document.write( "0 = 2L-2W-4 = -4L+8W-32\r\n" );
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document.write( "So we have the two equations:\r\n" );
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document.write( " 2L-2W- 4 = 0 \r\n" );
document.write( "-4L+8W-32 = 0\r\n" );
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document.write( " 2L-2W =  4  \r\n" );
document.write( "-4L+8W = 32\r\n" );
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document.write( "Solve that system of equations and get:\r\n" );
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document.write( "L = 12 cm²\r\n" );
document.write( "W = 10 cm²\r\n" );
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document.write( "Edwin

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