SOLUTION: A triangle has two sides of lengths 7 and 12 what value could the third side be?

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Question 481478: A triangle has two sides of lengths 7 and 12 what value could the third side be?

Found 3 solutions by cleomenius, richard1234, MathTherapy:
Answer by cleomenius(959)   (Show Source):
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Between 6 and 18.
By the triangle inequality theorem, the sum of any two sides of a triangle must exceed the third side.
Cleomenius.

Answer by richard1234(7193)   (Show Source):
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Technically between 5 and 19 (excluding the endpoints) because the third side length does not necessarily need to be an integer.

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!
A triangle has two sides of lengths 7 and 12 what value could the third side be?

Based on the triangle inequality theorem, the third side is greater than the difference between the other two sides, but less than their sum.

In other words, in this case, the third side is between 5 (12 - 7) and 19 (7 + 12), non-inclusive. This means that the third side can take on any REAL number that is greater than 5, but less than 19.

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