Which best describes the triangle or triangles, if any, that can be formed with sides measuring 60 centimeters, 100 centimeters, and 40 centimeters?

Steps to Solve

1. Apply the Triangle Inequality Theorem
   To determine if a triangle can be formed, we use the triangle inequality theorem. This states that the sum of the lengths of any two sides must be greater than the length of the remaining side. We need to check all three combinations.

2. Check the First Combination
   Check if the sum of the two shorter sides is greater than the longest side:
   $$ 60 + 40 > 100 $$
   Calculating gives:
   $$ 100 > 100 $$
   This condition is not satisfied (it must be strictly greater).

3. Check the Second Combination
   Check the first and longest side with the second side:
   $$ 60 + 100 > 40 $$
   Calculating gives:
   $$ 160 > 40 $$
   This condition is satisfied.

4. Check the Third Combination
   Lastly, check the two longer sides:
   $$ 100 + 40 > 60 $$
   Calculating gives:
   $$ 140 > 60 $$
   This condition is also satisfied.

5. Determine Conclusion
   Since one of the triangle inequality conditions is not satisfied (the first one), a triangle cannot be formed with sides measuring 60 cm, 100 cm, and 40 cm.