document.write( "Question 355788: how to find the range for the measure of the third side of a triangle given the measures of two sides
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Algebra.Com's Answer #254046 by Edwin McCravy(20060) $\"\"$ $\"About$

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how to find the range for the measure of the third side of a triangle given the
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document.write( "Let the third side be x.\r\n" );
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document.write( "Then we use the fact that the sum of any two sides of a triangle must be\r\n" );
document.write( "greater than the other side.\r\n" );
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document.write( "So if the sides are 8, 13 and x then we must have all three of these:\r\n" );
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document.write( "The third one  is automatically taken care of by , so we can\r\n" );
document.write( "ignore that one and just have\r\n" );
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document.write( "which can be written as  5 < x < 21\r\n" );
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document.write( "So the range for the measure of the third side x is {x| 5 < x < 21} in set\r\n" );
document.write( "builder notation  or (5,21) in interval notation.\r\n" );
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document.write( "There is an easier way if you learn it.\r\n" );
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document.write( "Given the measures of two sides of a triangle, the measure of the third side is\r\n" );
document.write( "between their difference (in absolute value) and their sum, exclusive of each.\r\n" );
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document.write( "So using that rule 13-8 < x < 13+8\r\n" );
document.write( "                      5 < x < 21, or (5,21)\r\n" );
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document.write( "Edwin

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