Can a triangle be formed with side lengths 6, 9, 12? Explain.
a) No, because 12 − 9 < 6
b) Yes, because 6 + 9 > 12
c) Yes, because 12 − 9 < 6
d) No, because 6 + 9 > 12
c) Yes, because 12 − 9 < 6
To determine if a triangle can be formed with given side lengths, we need to apply the triangle inequality theorem, which states that the sum of any two side lengths of a triangle must be greater than the third side length.
In this case, if we consider the side lengths 6, 9, and 12, we can see that 12 - 9 (3) is less than 6. This violates the triangle inequality theorem, meaning that a triangle cannot be formed with these side lengths.
Therefore, the correct answer is d) No, because 6 + 9 > 12