To determine the length of the third side of a triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that the first two sides measure 10 and 12, let's consider the possibilities for the length of the third side:
1) If the third side is less than 10, the sum of the first two sides (10 + 12 = 22) would be greater than the third side. This is not possible.
2) If the third side is equal to 10, the sum of the first two sides (10 + 12 = 22) would be equal to the third side. This is not possible.
3) If the third side is greater than 10 but less than 12, the sum of the first two sides (10 + 12 = 22) would be greater than the third side. This is possible.
4) If the third side is equal to 12, the sum of the first two sides (10 + 12 = 22) would be equal to the third side. This is not possible.
5) If the third side is greater than 12, the sum of the first two sides (10 + 12 = 22) would still be less than the third side. This is not possible.
Therefore, the possible length of the third side is any value between 10 and 12 (exclusive).
Determine the length of the third side of a triangle from the choices provided if the first two sides measure 10 and 12
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