document.write( "Question 1040265: A triangle has a perimeter of
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Algebra.Com's Answer #655051 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "A triangle has a perimeter of 24 inches. The medium side is
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document.write( "Let x be the shortest side length, in inches.\r\n" );
document.write( "Then the medium side is (x + 3) inches,\r\n" );
document.write( "while the longest side is 5x inches long.\r\n" );
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document.write( "The perimeter is the sum  x + (x+3) + 5x, so your equation is\r\n" );
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document.write( "x + (x+3) + 5x = 24.\r\n" );
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document.write( "Simplify and solve it\r\n" );
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document.write( "7x + 3 = 24  --->  7x = 24-3  --->  7x = 21  --->  x = \"21%2F7\" = 3.\r\n" );
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document.write( "Hence, the shortest side length is 3 in.\r\n" );
document.write( "Then the medium side is x + 3 = 3 + 3 = 6 in\r\n" );
document.write( "and the longst side is 5x = 5*3 = 15 in.\r\n" );
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document.write( "Now check if such a triangle does exist.\r\n" );
document.write( "The sum of the lengths of the shortest and the medium sides is 3 + 6 in = 9 in.\r\n" );
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document.write( "It is less than the length 15 in of the longest side.\r\n" );
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document.write( "Hence, the triangle (3,6,15) actually doesn't exist.\r\n" );
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document.write( "It implies that the problem HAS NO solution.\r\n" );
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document.write( "Answer.  The problem HAS NO solution.  Such a triangle doesn't exist.\r\n" );
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