### Instruction: What is the smallest possible perimeter, in units, of a triangle whose side-length measures are consecutive integer values?### Response: I know that the perimeter of a triangle is the sum of the lengths of its three sides.
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.
So I need to find the smallest set of three consecutive integers that satisfy the triangle inequality.
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.