document.write( "Question 156307: A box contains one 2-inch rod, one 3-inch rod, one 4-inch rod, and one 5-inch rod. What is the maximum number of different triangles that can be made using these rods as sides? \n" ); document.write( "
Algebra.Com's Answer #115260 by Edwin McCravy(20055)\"\" \"About 
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A box contains one 2-inch rod, one 3-inch rod, one 4-inch rod, and one 5-inch rod. What is the maximum number of different triangles that can be made using these rods as sides?
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document.write( "In order for a, b, and c to be the sides of a triangle,\r\n" );
document.write( "all three of these must be true:\r\n" );
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document.write( "a + b > c, a + c > b, and b + c > a\r\n" );
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document.write( "That is, in any triangle, the sum of any two sides must\r\n" );
document.write( "be greater than the third side.\r\n" );
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document.write( "We will make all combinations of three of the rods\r\n" );
document.write( "and eliminate any that can't be triangles:\r\n" );
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document.write( "1.  2-inch, 3 inch, 4-inch\r\n" );
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document.write( "That is a triangle, because 2+3 > 4, 2+4 > 3, and 3+4 > 2\r\n" );
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document.write( "2.  2-inch, 3 inch, 5-inch\r\n" );
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document.write( "This is NOT a triangle because even though 2+5>3, and 3+5>2,\r\n" );
document.write( "however 2+3 is NOT GREATER than 5, for it's EQUAL to 5. And\r\n" );
document.write( "unless all three are true, they cannot form a triangle. \r\n" );
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document.write( "3.  2-inch, 4 inch, 5-inch\r\n" );
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document.write( "That is a triangle, because 2+4 > 5, 2+5 > 4, and 4+5 > 2\r\n" );
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document.write( "4.  3-inch, 4 inch, 5-inch\r\n" );
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document.write( "That is a triangle, because 3+4 > 5, 3+5 > 4, and 4+5 > 3\r\n" );
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document.write( "So a maximum of 3 triangles can be formed with those\r\n" );
document.write( "rods, since we eliminated case 2 above.\r\n" );
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document.write( "Edwin
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