Question

"Determine if a triangle can be formed with the given side lengths. Complete the reasoning.

28 cm, 9 cm, 30 cm
Can a triangle have these three side lengths?"

A) Yes, a triangle can be formed with these side lengths.

B) No, a triangle cannot be formed with these side lengths.

Answer 1

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.