document.write( "Question 1172906: Rectangles A and B are both four times as long as they are wide and the length of rectangle A is three times the length of rectangle B. If the difference in the perimeters is 16cm, find the dimensions of each rectangle. \n" ); document.write( "
Algebra.Com's Answer #798056 by Edwin McCravy(20055)\"\" \"About 
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Rectangles A and B are both four times as long as they are wide.
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document.write( "They are similar (have the same shape)\r\n" );
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document.write( "Let w = the small rectangle's width.\r\n" );
document.write( "Then 4w = the small rectangle's length.\r\n" );
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the length of rectangle A is three times the length of rectangle B
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document.write( "Since 4w = the small rectangle's length,\r\n" );
document.write( "3(4w) or 12w = the length of the large rectangle's length.\r\n" );
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document.write( "Since the rectangles are similar, the width of the larger triangle is\r\n" );
document.write( "also three times the width of the smaller rectangle.\r\n" );
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document.write( "So 3w = the width of the larger rectangle.\r\n" );
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If the difference in the perimeters is 16cm,
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document.write( "The formula for the perimeter is \"2%2Alength%2B2%2Awidth\"\r\n" );
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document.write( "\"%282%2812w%29%5E%22%22+%2B+2%283w%29%29-%282%284w%29%5E%22%22+%2B+2%28w%29%29=16\"\r\n" );
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document.write( "\"%2824w%2B6w%29-%288w%2B2w%29=16\"\r\n" );
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document.write( "\"30w+-+10w+=+16\"\r\n" );
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document.write( "\"20w=16\"\r\n" );
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document.write( "\"w=16%2F20\"\r\n" );
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document.write( "\"w=4%2F5\"\r\n" );
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document.write( "So the width of the smaller rectangle B is 4/5 = 0.8 cm\r\n" );
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document.write( "4w = the small rectangle's length = 4(4/5) = 16/5 - 3.2 cm\r\n" );
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document.write( "3w = the width of the larger rectangle = 3(4/5) = 12/5 = 2.4 cm\r\n" );
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document.write( "12w = the length of the large rectangle's length = 12(4/5) = 48/5 = 9.6 cm\r\n" );
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document.write( "\"system%28L=4W%2C+l=4w%2C%282W%2B2L%29-%282w%2B2l%29=16%2C+L=3l%29\"\r\n" );
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document.write( "Edwin
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