document.write( "Question 815188: a square piece of paper is cut into six rectangle pieces
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Algebra.Com's Answer #490779 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "There are many different solutions to this problem,\r\n" );
document.write( "depending on how you cut the rectangle\r\n" );
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document.write( "If you cut it into equal rectangles like this:\r\n" );
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document.write( "where each has perimeter 2L+2W,\r\n" );
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document.write( "then the sum of the perimeters is 6(2L+2W)\r\n" );
document.write( "6(2L+2W) = 120\r\n" );
document.write( " 12L+12W = 120\r\n" );
document.write( "     L+W = 10\r\n" );
document.write( "       L = 10-W\r\n" );
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document.write( "      3W = 2L\r\n" );
document.write( "      3W = 2(10-W)\r\n" );
document.write( "      3W = 20-2W\r\n" );
document.write( "      5W = 20\r\n" );
document.write( "       W = 4 \r\n" );
document.write( "       L = 10-W\r\n" );
document.write( "       L = 10-4\r\n" );
document.write( "       L = 6\r\n" );
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document.write( "So the a side of the square is 3W = 2L = 3(4) = 2(6) = 12\r\n" );
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document.write( "So the area of a 12×12 square is 144cm²\r\n" );
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document.write( "However if you cut it into 6 equal pieces lke this,\r\n" );
document.write( "which is what the other tutor did, you get a smaller area.\r\n" );
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document.write( "Then up to a certain point, it's like the above:\r\n" );
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document.write( "where each has perimeter 2L+2W,\r\n" );
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document.write( "then the sum of the perimeters is 6(2L+2W)\r\n" );
document.write( "6(2L+2W) = 120\r\n" );
document.write( " 12L+12W = 120\r\n" );
document.write( "     L+W = 10\r\n" );
document.write( "       L = 10-W\r\n" );
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document.write( "But this time\r\n" );
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document.write( "      6W = L  \r\n" );
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document.write( "      6W = 10-W\r\n" );
document.write( "      7W = 10\r\n" );
document.write( "       W = 10/7\r\n" );
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document.write( "And the side of the square is L = 6W = 6(10/7) = 60/7 cm\r\n" );
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document.write( "And the area of the square is (60/7)² = 3600/49 = 73.46938776 cm². \r\n" );
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document.write( "Now if you cut into 6 UNequal rectangles like this\r\n" );
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document.write( "You would get still a totally different answer.\r\n" );
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document.write( "Edwin

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