document.write( "Question 983972: Rectangle of perimeter 32 cm. if its length decreases 1 cm & its width increases 3 cm, it will be square. find area of square
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Algebra.Com's Answer #604765 by Edwin McCravy(20081)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Instead of doing your problem for you, I will do one exactly in every detail\r\n" );
document.write( "like yours and you can use it as a model to do yours by.  I will do this\r\n" );
document.write( "one instead:\r\n" );
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\n" ); document.write( "Rectangle of perimeter 38 cm. if its length decreases 2 cm & its width increases
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\n" ); document.write( "\n" ); document.write( ">>Rectangle of perimeter 38 cm<<
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document.write( "P = 2L + 2W\r\n" );
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document.write( "So we substitute 38 for P\r\n" );
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document.write( "38 = 2L + 2W   <-- that's one equation\r\n" );
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\n" ); document.write( ">>if its length decreases 2 cm<<
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document.write( "Then its new length will be L-2\r\n" );
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\n" ); document.write( ">>& its width increases 5 cm<<
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document.write( "Then its new width will be W+5\r\n" );
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\n" ); document.write( ">>it will be square<<
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document.write( "Then its length and width will be equal, so\r\n" );
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document.write( "\"%28matrix%282%2C1%2CNEW%2CLENGTH%29%29\"\"%22%22=%22%22\"\"%28matrix%282%2C1%2CNEW%2CWIDTH%29%29\"\r\n" );
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document.write( "L-2 = W+5      <-- That's another equation.\r\n" );
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document.write( "So we have this system of two equations and 2 unknowns to solve \r\n" );
document.write( "by substitution:\r\n" );
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document.write( "\"system%2838+=+2L+%2B+2W%2C+L-2=W%2B5%29\"\r\n" );
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document.write( "We can simplify the first equation,\r\n" );
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document.write( "38 = 2L + 2W\r\n" );
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document.write( "by dividing it through by 2, getting,\r\n" );
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document.write( "19 = L + W\r\n" );
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document.write( "We can simplify the second equation,\r\n" );
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document.write( "L - 2 = W + 5\r\n" );
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document.write( "by adding 2 to both sides:\r\n" );
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document.write( "    L = W + 7\r\n" );
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document.write( "Now the system is\r\n" );
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document.write( "\"system%2819+=+L+%2B+W%2C+L=W%2B7%29\"\r\n" );
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document.write( "Since the second equation is already solved for L, we\r\n" );
document.write( "substitute (W + 7) for L in the first equation, and get:\r\n" );
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document.write( "19 = (W + 7) + W\r\n" );
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document.write( "Remove the parentheses:\r\n" );
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document.write( "19 = W + 7 + W\r\n" );
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document.write( "Combine like terms on the right\r\n" );
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document.write( "19 = 2W + 7\r\n" );
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document.write( "Subtract 7 from both sides\r\n" );
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document.write( "12 = 2W\r\n" );
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document.write( "Divide both sides by 2\r\n" );
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document.write( " 6 = W\r\n" );
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document.write( "Substitute 6 for W in\r\n" );
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document.write( "    L = W + 7\r\n" );
document.write( "    L = 6 + 7\r\n" );
document.write( "    L = 13\r\n" );
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document.write( "So the original length was 13 cm and the original width 6 cm\r\n" );
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\n" ); document.write( ">>find area of square<<
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document.write( "So the new length will be L-2 or 13-2 = 11 cm\r\n" );
document.write( "And its new width will be W+5 or 6+5 = 11 cm\r\n" );
document.write( "So a side of the square will be 11 cm\r\n" );
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document.write( "So its area will be \r\n" );
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document.write( "A = (side)2 = 112 = 121 square centimeters.\r\n" );
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document.write( "Now do yours which is done exactly the same way, step by step.\r\n" );
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document.write( "Edwin
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