SOLUTION: A triangle has two sides of length 10 and 14. What value could the length of the third side be?

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Question 377757: A triangle has two sides of length 10 and 14. What value could the length of the third side be?
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A triangle has two sides of length 10 and 14. What value could the length of the third side be?
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It has to be greater than the difference, 14-10 = 4, and
it has to be less than the sum, 14+10 = 24
4 < s < 24
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!

The third side must be between:

a. the difference of the other two sides

 and 

b. the sum of the other two sides.

So the third side must be between

a. the difference of the other two sides 14-10 or 4 and
b. the sum of the other two sides 14+10 or 24.  

EXCLUSIVE of 4 and EXCLUSIVE of 24

So the answer is that if c is the third side, then 4 < c < 24 

Just think.  If the third side were 4 or less it would be too short to make a
triangle with the other two.  And if the third side were 24 or more it would be
too long to make a triangle with the other two.

Edwin


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