Final answer:
The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. Therefore, the possible lengths for the third side of the triangle with side lengths of 7 meters and 15 meters are 8 meters, 12 meters, and 22 meters.
Step-by-step explanation:
To determine the possible length of the third side of a triangle, we can 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.
For the given triangle with sides measuring 7 meters and 15 meters, we can test the possible lengths:
- If the third side is 6 meters, the sum of the other two sides would be 7 + 6 = 13 meters, which is less than 15 meters. Therefore, 6 meters cannot be the length of the third side.
- If the third side is 8 meters, the sum of the other two sides would be 7 + 8 = 15 meters, which is equal to 15 meters. Therefore, 8 meters could be the length of the third side.
- If the third side is 12 meters, the sum of the other two sides would be 7 + 12 = 19 meters, which is greater than 15 meters. Therefore, 12 meters could be the length of the third side.
- If the third side is 22 meters, the sum of the other two sides would be 7 + 22 = 29 meters, which is greater than 15 meters. Therefore, 22 meters could be the length of the third side.
Based on the Triangle Inequality Theorem, the possible lengths for the third side of the triangle are 8 meters, 12 meters, and 22 meters.