document.write( "Question 102689: There is a rectangle whose perimeter is 18 centimeters. If its length is decreased by 5 centimeters and it's width is increased by 12 centimeters, it's area is doubled. Find its length and width.\r
\n" ); document.write( "\n" ); document.write( "This Question is so hard to understand! Please help! \n" ); document.write( "
Algebra.Com's Answer #74820 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Let's take it step-by-step
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\n" ); document.write( "\"There is a rectangle whose perimeter is 18 centimeters.\"
\n" ); document.write( "Let the length and width be x & y
\n" ); document.write( "Perimeter:
\n" ); document.write( "2x + 2y = 18
\n" ); document.write( "Simplify, divide equation by 2
\n" ); document.write( "x + y = 9
\n" ); document.write( "y = (9-x); we substitute (9-x) for y
\n" ); document.write( "Find the area:
\n" ); document.write( "x(9-x) = -x^2 + 9x
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\n" ); document.write( "\"If its length is decreased by 5 centimeters and it's width is increased by 12 centimeters, it's area is doubled. Find its length and width.\"
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\n" ); document.write( "New length: (x-5)
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\n" ); document.write( "New width:
\n" ); document.write( "(9-x) + 12
\n" ); document.write( "(-x + 21)
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\n" ); document.write( "New area (double the old area): 2(-x^2 + 9x) = -2x^2 + 18x
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\n" ); document.write( "New width * new length = twice the area
\n" ); document.write( "(-x + 21)*(x - 5) = -2x^2 + 18x
\n" ); document.write( "FOIL the left side
\n" ); document.write( "-x^2 + 5x + 21x -105 = -2x^2 + 18
\n" ); document.write( "-x^2 + 26x - 105 = -2x^2 + 18x
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\n" ); document.write( "Combine to form a quadratic equation:
\n" ); document.write( "-x^2 + 2x^2 + 26x - 18x - 105 = 0
\n" ); document.write( "x^2 + 8x - 105 = 0
\n" ); document.write( "Factor this to
\n" ); document.write( "(x + 15)*(x - 7) = 0
\n" ); document.write( "x = +7 is the original length (only the positive solution is used)
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\n" ); document.write( "Remember y = 9 - x:
\n" ); document.write( "y = 9 - 7
\n" ); document.write( "y = 2 is the original width
\n" ); document.write( "Original area = 7 * 2 = 14 sq/cm
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\n" ); document.write( "New length and width:
\n" ); document.write( "L = 7 - 5 = 2 cm
\n" ); document.write( "W = 21 - 7 = 14
\n" ); document.write( "2 * 14 = 28 sq/cm, double the original
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\n" ); document.write( "Could you follow this OK?\r
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