What is the smallest possible perimeter, in units, of a triangle whose side-length measures are consecutive integer values?
I also know that the triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side. This means that I cannot have a triangle with sides 1, 2, and 3, for example, because 1 + 2 = 3, which is not greater than 3. I can start by trying 2, 3, and 4. 2 + 3 = 5, which is greater than 4, so that's good. 3 + 4 = 7, which is greater than 2, so that's also good. 4 + 2 = 6, which is greater than 3, so that's good too. Therefore, 2, 3, and 4 are the smallest possible consecutive integers that form a triangle. The perimeter of this triangle is 2 + 3 + 4 = 9 units. 