document.write( "Question 829869: A square and a rectangle each has a perimeter of 48 m. The difference between the areas of two figures is 4 m2. Find the dimensions of the rectangle. \n" ); document.write( "
Algebra.Com's Answer #500254 by math-vortex(648)\"\" \"About 
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "A square and a rectangle each has a perimeter of 48 m. The difference between the areas of \r\n" );
document.write( "two figures is 4 square meters. Find the dimensions of the rectangle.\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "Consider the square with perimeter 48m. \r\n" );
document.write( "Let x be the length of each side.\r\n" );
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document.write( "The perimeter is the distance around, or 4x.\r\n" );
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document.write( "4x = 48\r\n" );
document.write( "x = 12\r\n" );
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document.write( "The length of each side is 12m.\r\n" );
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document.write( "The area of the square is the side length times the side length, or x*x. \r\n" );
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document.write( "12*12 = 144\r\n" );
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document.write( "The area of the square is 144 square meters.\r\n" );
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document.write( "We are told that the difference between the area of the square and the rectangle is 4 square \r\n" );
document.write( "meters. Then the area of the rectangle must be 4 more or 4 less. \r\n" );
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document.write( "For now, assume that the rectangle has the lesser area, or 140 square meters.\r\n" );
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document.write( "The formula for the area of a rectangle is length times width, or L*W. We have\r\n" );
document.write( "L*W = 140.\r\n" );
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document.write( "We also know that the perimeter of the rectangle is 48. We have\r\n" );
document.write( "2L + 2W = 48\r\n" );
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document.write( "We have two equations with two variables. Solve for L and W.\r\n" );
document.write( "Solve the first equation for L.\r\n" );
document.write( "L*W = 140\r\n" );
document.write( "L = 140/W\r\n" );
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document.write( "Substitute 140/W for L in the second equation.\r\n" );
document.write( "2L + 2W = 48\r\n" );
document.write( "2(140/W) + 2W = 48\r\n" );
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document.write( "Solve for W.\r\n" );
document.write( "280/W + 2W = 48\r\n" );
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document.write( "Subtract 2W from both sides.\r\n" );
document.write( "280/W = -2W + 48\r\n" );
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document.write( "Multiply both sides by W.\r\n" );
document.write( "280 = -2W^2 + 48W\r\n" );
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document.write( "This is a quadratic equation. Solve by factoring.\r\n" );
document.write( "2W^2 - 48W + 280 = 0\r\n" );
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document.write( "Divide each term by 2.\r\n" );
document.write( "W^2 - 24W + 140 = 0\r\n" );
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document.write( "(W - 14)(W - 10) = 0\r\n" );
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document.write( "W = 14 or W = 10\r\n" );
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document.write( "The width of the rectangle is 10m or 14m.\r\n" );
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document.write( "If the width of the rectangle is 10m, then its length is 14m because \r\n" );
document.write( "2L + 2W  = 2(10) + 2(14) = 48\r\n" );
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document.write( "The dimensions of the rectangle are 10m by 14m.\r\n" );
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document.write( "You can work out the dimensions of the rectangle if it has the larger area. Then your\r\n" );
document.write( "equations will be\r\n" );
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document.write( "L*W = 148\r\n" );
document.write( "2L + 2W = 48\r\n" );
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document.write( "I'll leave that to you.\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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