Question

Which lengths of sides will form a triangle? A. 5 cm, 9 cm, 11 cm B. 7 cm, 4 cm, 12 cm C. 11 cm, 21 cm, 14 cm D. 15 cm, 4 cm, 22 cm

Answer 1

The only selection from A, B, C, and D that can form a triangle based on the Triangle Inequality Theorem is option A (5 cm, 9 cm, 11 cm). The lengths in the other options do not meet the requirements of the theorem.

Step-by-step explanation:

The subject of this question is in the realm of Mathematics, specifically geometry. In regards to forming a triangle with given lengths of sides, it's crucial to know 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.

Let's evaluate each option:

1. A. 5 cm, 9 cm, 11 cm: 5+9 > 11, 5+11 > 9, and 9+11 > 5; thus, these lengths can form a triangle.
2. B. 7 cm, 4 cm, 12 cm: 7+4 is not greater than 12; therefore, these lengths cannot form a triangle.
3. C. 11 cm, 21 cm, 14 cm: 11+14 is not greater than 21; thus, these lengths cannot form a triangle.
4. D. 15 cm, 4 cm, 22 cm: 15 + 4 is not greater than 22, so these lengths cannot form a triangle either.

Learn more about Triangle Inequality Theorem