document.write( "Question 234188: Given two sides with lengths 34 and 14, which of these lengths would NOT work for the third side of a triangle? 18, 34, 44, 22, 40 \n" ); document.write( "
Algebra.Com's Answer #172715 by Edwin McCravy(20056)![]() ![]() You can put this solution on YOUR website! Given two sides with lengths 34 and 14, which of these lengths would NOT work for the third side of a triangle? 18, 34, 44, 22, 40. \n" ); document.write( " \n" ); document.write( "The sum of two sides of a triangle must always be greater than the third side.\r \n" ); document.write( "\n" ); document.write( "So we'll make three checks on each choice.\r \n" ); document.write( "\n" ); document.write( "Let's begin by trying 18.\r \n" ); document.write( "\n" ); document.write( "Then the sides are 34, 14 and 18.\r \n" ); document.write( "\n" ); document.write( "Add 34+14, that's 48, and that's greater than the third side, 18, so that \n" ); document.write( "checks.\r \n" ); document.write( "\n" ); document.write( "Add 34+18, that's 52, and that's greater than the third side, 14, so that \n" ); document.write( "checks.\r \n" ); document.write( "\n" ); document.write( "Add 14+18, that's 32, and that's NOT greater than the third side, 34, \n" ); document.write( "so that DOES NOT check. So 18 will NOT work for the third side of \n" ); document.write( "a triangle with sides 34 and 14. \r \n" ); document.write( "\n" ); document.write( "-----------------\r \n" ); document.write( "\n" ); document.write( "Let's try 34.\r \n" ); document.write( "\n" ); document.write( "Then the sides are 34, 14 and 34.\r \n" ); document.write( "\n" ); document.write( "Add 34+14, that's 48, and that's greater than the third side, 34, so that \n" ); document.write( "checks.\r \n" ); document.write( "\n" ); document.write( "Add 34+34, that's 68, and that's greater than the third side, 14, so that \n" ); document.write( "checks.\r \n" ); document.write( "\n" ); document.write( "Add 14+34, that's 48, and that's greater than the third side, 34, so that \n" ); document.write( "checks.\r \n" ); document.write( "\n" ); document.write( "So 34 DOES work for a third side for a triangle with sides 34 and 14.\r \n" ); document.write( "\n" ); document.write( "-------------------\r \n" ); document.write( "\n" ); document.write( "Let's try 44.\r \n" ); document.write( "\n" ); document.write( "Then the sides are 34, 14 and 44.\r \n" ); document.write( "\n" ); document.write( "Add 34+14, that's 48, and that's greater than the third side, 44, so that \n" ); document.write( "checks.\r \n" ); document.write( "\n" ); document.write( "Add 34+44, that's 78, and that's greater than the third side, 14, so that \n" ); document.write( "checks.\r \n" ); document.write( "\n" ); document.write( "Add 14+44, that's 58, and that's greater than the third side, 34, so that \n" ); document.write( "checks.\r \n" ); document.write( "\n" ); document.write( "So 44 DOES work for a third side for a triangle with sides 34 and 14.\r \n" ); document.write( "\n" ); document.write( "-------------------------\r \n" ); document.write( "\n" ); document.write( "Let's try 22.\r \n" ); document.write( "\n" ); document.write( "Then the sides are 34, 14 and 22.\r \n" ); document.write( "\n" ); document.write( "Add 34+14, that's 48, and that's greater than the third side, 22, so that \n" ); document.write( "checks.\r \n" ); document.write( "\n" ); document.write( "Add 34+22, that's 56, and that's greater than the third side, 14, so that \n" ); document.write( "checks.\r \n" ); document.write( "\n" ); document.write( "Add 14+22, that's 36, and that's greater than the third side, 34, so that \n" ); document.write( "checks.\r \n" ); document.write( "\n" ); document.write( "So 22 DOES work for a third side for a triangle with sides 34 and 14.\r \n" ); document.write( "\n" ); document.write( "-------------------\r \n" ); document.write( "\n" ); document.write( "Let's try 40.\r \n" ); document.write( "\n" ); document.write( "Then the sides are 34, 14 and 40.\r \n" ); document.write( "\n" ); document.write( "Add 34+14, that's 48, and that's greater than the third side, 40, so that \n" ); document.write( "checks.\r \n" ); document.write( "\n" ); document.write( "Add 34+40, that's 74, and that's greater than the third side, 14, so that \n" ); document.write( "checks.\r \n" ); document.write( "\n" ); document.write( "Add 14+40, that's 54, and that's greater than the third side, 34, so that \n" ); document.write( "checks.\r \n" ); document.write( "\n" ); document.write( "So 40 DOES work for a third side for a triangle with sides 34 and 14.\r \n" ); document.write( "\n" ); document.write( "---------------------\r \n" ); document.write( "\n" ); document.write( "So the only choice that won't work for a third side of a triangle with \n" ); document.write( "sides 34 and 14 is 18.\r \n" ); document.write( "\n" ); document.write( "Why is that?\r \n" ); document.write( "\n" ); document.write( "Suppose you had a triangle ABC drawn on the ground where AB is 34 feet, \n" ); document.write( "AC is 14 feet, and BC is 18 feet. Since the shortest distance from A \n" ); document.write( "to B is the straight line segment connecting them, namely AB, or 34 feet. \n" ); document.write( "But if there were such a triangle it would be shorter to walk from A to C, \n" ); document.write( "and then turn and walk from C to B, since AC is 14 feet and BC is 18 feet, \n" ); document.write( "so that would be only 32 feet. So there can't be any such triangle.\r \n" ); document.write( "\n" ); document.write( "Edwin \n" ); document.write( " \n" ); document.write( " |