5,2,2 cannot represent the length units of the side of a triangle
5+2>2
5+2>2
2+2< />
so, the last equation doesn't match with the property

Introduction:
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the Triangle Inequality Theorem. To determine which of the given triplets cannot represent the lengths of the sides of a triangle, we need to check if this inequality holds true for each triplet.

Analysis:
Let's analyze each triplet one by one:

1. (5,2,2):
- The sum of the two smaller sides is 2 + 2 = 4.
- However, the length of the longest side is 5, which is greater than the sum of the other two sides.
- Therefore, this triplet cannot represent the lengths of the sides of a triangle.

2. (3,4,5):
- The sum of the two smaller sides is 3 + 4 = 7.
- The length of the longest side is 5, which is not greater than the sum of the other two sides.
- Therefore, this triplet can represent the lengths of the sides of a triangle.

3. (5,12,13):
- The sum of the two smaller sides is 5 + 12 = 17.
- The length of the longest side is 13, which is greater than the sum of the other two sides.
- Therefore, this triplet can represent the lengths of the sides of a triangle.

4. (4,7,8):
- The sum of the two smaller sides is 4 + 7 = 11.
- The length of the longest side is 8, which is greater than the sum of the other two sides.
- Therefore, this triplet can represent the lengths of the sides of a triangle.

Conclusion:
Out of the given triplets, (5,2,2) cannot represent the lengths of the sides of a triangle, as it violates the Triangle Inequality Theorem. The other triplets (3,4,5), (5,12,13), and (4,7,8) satisfy the theorem and can represent the lengths of the sides of a triangle.