document.write( "Question 636227: The area of a 6 m by 4 m rectangle is to be doubled. By what equal amount must each dimension be increased? \n" ); document.write( "
Algebra.Com's Answer #400931 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( "The area of a 6 m by 4 m rectangle is to be doubled. By what equal amount must each dimension be increased?\r\n" );
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document.write( "A solution:\r\n" );
document.write( "Let x be the amount by which each dimension is increased.\r\n" );
document.write( "Then the side lengths of the larger rectangle are 6+x and 4+x meters.\r\n" );
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document.write( "The area of the smaller rectangle is 6*4=24 square meters.\r\n" );
document.write( "The area of the larger rectangle is doubled, so its area is 24*2=48 square meters.\r\n" );
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document.write( "Now we use the formula for the area of a rectangle (length times width equals area) to write an equation and solve for x.\r\n" );
document.write( "(6+x)*(4+x) = 48\r\n" );
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document.write( "Use the distributive property to simplify the left side.\r\n" );
document.write( "24+6x+4x+x^2 = 48\r\n" );
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document.write( "Rearrange and combine terms.\r\n" );
document.write( "x^2 + 10x + 24 = 48\r\n" );
document.write( "x^2 + 10x - 24 = 0\r\n" );
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document.write( "Factor. You want two factors whose sum is 10 and whose product is -24. The factors are -2 and 12.\r\n" );
document.write( "(x + 12)(x - 2) = 0\r\n" );
document.write( "x + 12 = 0 OR x - 2 = 0\r\n" );
document.write( "x = -12 or x = 2\r\n" );
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document.write( "x = -12 has no meaning in this problem since the rectangle cannot have negative dimensions.\r\n" );
document.write( "x = 2 means that we increase each side length by 2 meters.\r\n" );
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document.write( "Check.\r\n" );
document.write( "The side lengths of the larger rectangle are 6+2=8 and 4+2=6. The area of the larger rectangle is 8*6=48. The area of the large rectangle is double the area of the smaller one \r\n" );
document.write( "since 48 is double 24.\r\n" );
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document.write( "That's it. Feel free to email me if you have questions about the solution.\r\n" );
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document.write( "Ms.Figge\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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