SOLUTION: The lengths of 2 sides of a triangle are 4 and 9. What is the range of possible lengths for the 3rd side? How do you set up these problems, and how do you solve them?

Question 541701: The lengths of 2 sides of a triangle are 4 and 9. What is the range of possible lengths for the 3rd side?
How do you set up these problems, and how do you solve them?
Answer by neatmath(302) (Show Source): You can put this solution on YOUR website!

This kind of triangle problem is fairly simple.

There is a rule for triangle side lengths.

Each leg must be between the difference and sum of the other two legs (non-inclusively).

So, since your two legs are 4 and 9, we have:

Therefore the possible length of the third side of your triangle would be:

any real number between 5 and 13 (not including 5 and 13 of course). Or

If the 3rd side of your triangle was 5 or 13, it would be a degenerate triangle which appeared to be a straight line.

I hope this helps!

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