Final answer:
To find the smallest possible whole-number length for the third side of a triangle with two sides of length 5 and 4, apply the Triangle Inequality Theorem. The smallest possible whole-number length for the third side is 2.
Step-by-step explanation:
To find the smallest possible whole-number length for the third side of a triangle with two sides of length 5 and 4, we need to apply the Triangle Inequality Theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, the third side must be larger than the difference between the lengths of the other two sides, but smaller than the sum of their lengths.
In this case, the difference between the lengths of the two sides is 5 - 4 = 1, and the sum of their lengths is 5 + 4 = 9. Therefore, the smallest possible whole-number length for the third side is 2, as it is larger than 1 and smaller than 9.