According to the triangle inequality theorem, for a triangle with side lengths a, b, and c, the sum of any two sides must be greater than the third side.
In this case, the first two sides measure 4 and 6. Let's consider the possible values for the third side to form a triangle:
1) If the third side is less than 2, the sum of the first two sides would be less than the third side, violating the triangle inequality. Therefore, the third side cannot be less than 2.
2) If the third side is equal to 2, the sum of the first two sides would be equal to the third side (4 + 6 = 2), violating the triangle inequality. Therefore, the third side cannot be equal to 2.
3) If the third side is between 2 and 4, the sum of the first two sides would be less than the third side, violating the triangle inequality. Therefore, the third side cannot be between 2 and 4.
4) If the third side is equal to 4, the sum of the first two sides would be equal to the third side (4 + 6 = 4), violating the triangle inequality. Therefore, the third side cannot be equal to 4.
5) If the third side is between 4 and 6, the sum of the first two sides would be less than the third side, violating the triangle inequality. Therefore, the third side cannot be between 4 and 6.
6) If the third side is equal to 6, the sum of the first two sides would be equal to the third side (4 + 6 = 6), violating the triangle inequality. Therefore, the third side cannot be equal to 6.
7) If the third side is greater than 6, the sum of the first two sides would be greater than the third side, satisfying the triangle inequality. Therefore, the third side could be any value greater than 6.
In conclusion, if the first two sides measure 4 and 6, the third side could be any value greater than 6 in order to form a valid triangle.
Apply the triangle inequality therom and determine which option could be the third side of a triangle if the first two sides measure 4 and 6
1 answer