David W. answered • 07/15/15
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The diagram may or may not help to answer this question.
The more important rule is that, in order to form a triangle, any two sides put together must be longer than the third side (try this with short sticks, straws, etc.).
Let the third side be of length x.
So, x must be an integer and it is neither 8 nor 11 and it is the longest side (x>8 and x>11).
8+11 > x, that is, x < 19
x+8 > 11, that is, x > 3
x+11 > 8, that is, x > -3 (but as a positive integer, that means x>0)
O.K., what choices do we have that meet all the criteria we just listed?
12, 13, 14, 15, 16, 17, 18
You may pick any one of those.
David W.
Andrew M. has the facts absolutely correct!
However, in teaching, we consider (1) the subject, (2) the student, and (3) the style.
The subject is pretty easy for most tutors (they might even skip topics thinking that everyone knows the information. I learned that shortcuts make computer programs much faster, but much more difficult to read/understand/modify -- and what's a few more milliseconds of computer time compared to programmer's salary?
Then the student -- Along with the problem statement, Anna expresses her typical frustration with not getting the right answer (also see her other problem posts). The cold, hard fact is, "If the student has not learned, then the teacher has not taught." It is not what I do, as the teacher/tutor, but what the student does as a result of what I do that matters.
Then style -- this forum has verbose, terse, simple, complex, friendly, obnoxious, etc., etc. posts (both problems and answers). There is very little that I've read here that I could include in a textbook or in an on-line/tablet/phone ap for teaching. Of course, I want graphics, color, animation, sound, etc. -- and lots and lots of intelligent interaction.
If Andrew, or I, or any other tutor can help Anna with her math problem that's great. If anyone can help her with her frustration, that may be even more valuable (because, happy students learn more just like happy employees are more productive). And -- if, somehow, Anna gets enough confidence such that she can tackle her homework without a tutor, we have fulfilled our mission.
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07/15/15
Anna L.
Thank you so much to both of you!
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07/16/15
Andrew M.
07/15/15