SOLUTION: A triangle has integral factors of 8, 13, and n. What is the median of the possible values of n.

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Question 311173: A triangle has integral factors of 8, 13, and n. What is the median of the possible values of n.
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
A triangle has integral factors of 8, 13, and n. What is the median of the possible values of n. 

If any triangle's sides are a,b, and c, then

system%28a+%2B+b+%3E+c%2C%0D%0Aa+%2B+c+%3E+b%2C%0D%0Ab+%2B+c+%3E+a%29

So

system%288+%2B+13+%3E+n%2C%0D%0A8+%2B+n+%3E+13%2C%0D%0A13+%2B+n+%3E+8%29

system%2821+%3E+n%2C%0D%0An+%3E+5%2C%0D%0An+%3E+-5%29

We can ignore the third one, since it is implied by the middle one:

system%2821+%3E+n%2C%0D%0An+%3E+5%29

That is the same as:

5%3Cn%3C21

So n can be any of these 15 values (in order) 

6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

The median of an odd number of numbers is the one right smack
in the middle when they are arranged from smallest to largest,
or vice-versa.  That is the number I have colored red, which is 13.

Edwin