Two sides of a triangle are each $8$ units long. If the third side has a whole number length, what is the greatest possible perimeter, in units, for the triangle?
The Triangle Inequality says that the sum of the lengths of any two sides must be greater than the length of the third side. That means $8+8=16$ must be greater than the length of the third side. The third side has a whole number length, so the greatest possible length is 15 units. That makes the perimeter $8+8+15=\boxed{31}$ units.