Final answer:
Using the Triangle Inequality Theorem, it is shown that a triangle cannot be formed with side lengths of 28 cm, 9 cm, and 30 cm because the sum of the two shorter sides (37 cm) is not greater than the length of the longest side (30 cm).
Step-by-step explanation:
To determine if a triangle can be formed with the given side lengths of 28 cm, 9 cm, and 30 cm, we use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
For the given side lengths:
28 cm + 9 cm > 30 cm?
No, because 37 cm is not greater than 30 cm.
28 cm + 30 cm > 9 cm?
Yes, because 58 cm is greater than 9 cm.
9 cm + 30 cm > 28 cm?
Yes, because 39 cm is greater than 28 cm.
Since one of the conditions fails to satisfy the Triangle Inequality Theorem, the answer is B) No, a triangle cannot be formed with these side lengths.