document.write( "Question 276507: The perimeter of a triangle is 15. The lengths of the sides are integers. If the length of one side is 6, what is the shortest possible length of another side of the triangle? \n" ); document.write( "

Algebra.Com's Answer #201501 by Edwin McCravy(20056) $\"\"$ $\"About$

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The perimeter of a triangle is 15. The lengths of the sides are integers. If the length of one side is 6, what is the shortest possible length of another side of the triangle?
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document.write( "Suppose the sides are a, b, and 6.  Then\r\n" );
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document.write( "By the three triangular inequalities:\r\n" );
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document.write( ", , \r\n" );
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document.write( "Since , \r\n" );
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document.write( "Substituting in the three triangular inequalities:\r\n" );
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document.write( ", , \r\n" );
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document.write( ", , \r\n" );
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document.write( "From  we have \r\n" );
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document.write( "     , or , and since a is an integer,\r\n" );
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document.write( "     {a>=2}}}\r\n" );
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document.write( "So 2 is the smallest integer a can be.  \r\n" );
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document.write( "From , we can also similarly show that 7 is the largest\r\n" );
document.write( "integer a can be.\r\n" );
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document.write( "We could have interchanged a and b and shown the same for b, so\r\n" );
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document.write( "the smallest integer either of the sides other than the side that is 6\r\n" );
document.write( "coul dbe is 2.\r\n" );
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document.write( "Edwin

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