document.write( "Question 664479: Given a set of three numbers 4,5,7 how can i find out if these numbers can be the lengths of the sides of a triangle.? \n" ); document.write( "
Algebra.Com's Answer #413340 by Edwin McCravy(20054)\"\" \"About 
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Given a set of three numbers 4,5,7 how can i find out if these numbers can be the lengths of the sides of a triangle.?
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document.write( "Suppose you were walking from A to C. There are two ways you could get there.\r\n" );
document.write( "1. You could go from A to B, and then go from B to C.\r\n" );
document.write( "or\r\n" );
document.write( "2. You could go straight from A to C  \r\n" );
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document.write( "Taking the straight line shortcut from A to C MUST be shorter than going \r\n" );
document.write( "around by B. So the distance from A straight to C must be less than the\r\n" );
document.write( "total distance going around by B.   That is true for any\r\n" );
document.write( "triangle.\r\n" );
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document.write( "It comes from the fact that the shortest distance between two \r\n" );
document.write( "points is always the straight line between them.\r\n" );
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document.write( "Three numbers can be the lengths of the sides of a triangle\r\n" );
document.write( "if the longest length is less than the sum of the two shorter\r\n" );
document.write( "lengths.\r\n" );
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document.write( "The smallest two numbers are 4 and 5.\r\n" );
document.write( "Add them. 4+5\r\n" );
document.write( "Get 9  \r\n" );
document.write( "The longest side 7 is shorter than 9, (the distance going around by B).\r\n" );
document.write( "Therefore 4,5,7 CAN be the lengths of the sides of a triangle.\r\n" );
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document.write( "[Note: 4,5,9 could not be the lengths of the sides of a triangle, because\r\n" );
document.write( "9 is not less than 4+5.\r\n" );
document.write( " Neither could 4,5,10, because 10 is not less than 4+5.    \r\n" );
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document.write( "Edwin
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