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Two sides of a triangle are 10 mm and 7 mm. Determine the length of the third side from the choices given.(1 point) Responses
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just find the third length
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GPT 3.5
We cannot determine the length of the third side without more information.
Answered by
GPT 3.5
To find the length of the third side, we need to use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that two sides of the triangle are 10 mm and 7 mm, let's consider the possible lengths for the third side:
1. If the third side is less than 3 mm, then the sum of the two smaller sides (7 mm and the third side) would be less than the remaining side of 10 mm, violating the triangle inequality theorem.
2. If the third side is 3 mm long, then the sum of the two smaller sides (7 mm and the third side) would be equal to the remaining side of 10 mm. In this case, the triangle would be a degenerate triangle, also violating the triangle inequality theorem.
3. If the third side is between 3 mm and 17 mm, then the sum of the two smaller sides would be greater than the remaining side of 10 mm. In this case, a valid triangle can be formed.
Therefore, the length of the third side can be any value between 3 mm and 17 mm, inclusive.
Given that two sides of the triangle are 10 mm and 7 mm, let's consider the possible lengths for the third side:
1. If the third side is less than 3 mm, then the sum of the two smaller sides (7 mm and the third side) would be less than the remaining side of 10 mm, violating the triangle inequality theorem.
2. If the third side is 3 mm long, then the sum of the two smaller sides (7 mm and the third side) would be equal to the remaining side of 10 mm. In this case, the triangle would be a degenerate triangle, also violating the triangle inequality theorem.
3. If the third side is between 3 mm and 17 mm, then the sum of the two smaller sides would be greater than the remaining side of 10 mm. In this case, a valid triangle can be formed.
Therefore, the length of the third side can be any value between 3 mm and 17 mm, inclusive.
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