document.write( "Question 124665: My question goes like this...\"With two sticks of length 6 cm. and 9cm., how many triangles can be formed with the two sticks and a third stick with integral length?\" \n" ); document.write( "
Algebra.Com's Answer #91462 by bucky(2189)\"\" \"About 
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The answer to this is based upon the fact that the sum of the two short sides of a triangle must
\n" ); document.write( "be greater than the long side.
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\n" ); document.write( "You are given two sides, of which 9 is the longer. Therefore, the third side must be greater
\n" ); document.write( "than 3. Why? because 6 + 3 just equals 9. If you laid the side 6 in a direct line with the side
\n" ); document.write( "3, they would form a line 9 units long which would just be congruent with the third side 9.
\n" ); document.write( "To form a triangle, the two short sides must together form a line that is longer than 9.
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\n" ); document.write( "But what happens if 9 is not the long side of the triangle? What happens if the unknown third
\n" ); document.write( "stick is the long side? This unknown long side must be shorter than 15, because the other two
\n" ); document.write( "sides (9 and 6) must add up to be longer than the third side. So, in integral values, the
\n" ); document.write( "third stick must be 14 or shorter.
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\n" ); document.write( "So the values of the third stick may be anywhere in the interval from 4 to 14 ... including
\n" ); document.write( "the values 4 and 14. If you count all the integers in this interval you will find that the
\n" ); document.write( "unknown stick can have the values 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14. So 11 triangles
\n" ); document.write( "can be formed.
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\n" ); document.write( "Hope this helps you to understand the problem.
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