document.write( "Question 375335: If the lengths of the sides of a triangle are consecutive integers could the perimter be a prime number? \n" ); document.write( "
Algebra.Com's Answer #266909 by EdwinMcCravy(4)\"\" \"About 
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If the lengths of the sides of a triangle are consecutive integers could the perimter be a prime number?
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document.write( "The only even prime number is 2, and that can't be the perimeter of a triangle\r\n" );
document.write( "with consecutive integer sides, so the perimeter must be odd in order to be a\r\n" );
document.write( "prime number.  So we cannot have the shortest side odd, the middle sized side\r\n" );
document.write( "even,  and the largest side odd, since the perimeter would then be even,\r\n" );
document.write( "since \"odd+even+odd=even\"\r\n" );
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document.write( "So the shortest side must be even, the medium-size side must be odd, and\r\n" );
document.write( "the longest side must be even, and that works since even+odd+even=odd.\r\n" );
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document.write( "So let the shortest side be 2n where n is any integer,\r\n" );
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document.write( "So the sides are 2n, 2n+1, and 2n+2.  That makes the perimeter be:\r\n" );
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document.write( "2n + (2n+1) + (2n+2)\r\n" );
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document.write( "So perimeter = 2n + 2n + 1 + 2n + 2\r\n" );
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document.write( "Perimeter = 6n + 3\r\n" );
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document.write( "Perimeter = 3(2n+1)\r\n" );
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document.write( "So the perimeter is always divisible by 3 so it cannot be prime.\r\n" );
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document.write( "The answer is NO.\r\n" );
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document.write( "Edwin
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