Question

triangle has side lengths 7 cm and 4 cm. What can you say about the length of the third side? A A third side cannot be found to complete this triangle. B The third side is longer than 4 cm and shorter than 7 cm. C The third side is longer than 3 cm and shorter than 11 cm. D No conclusion can be made about the third side.

Answer 1

The length of the third side in a triangle with sides of 7 cm and 4 cm must be longer than 3 cm and shorter than 11 cm, according to the Triangle Inequality Theorem.

Step-by-step explanation:

To determine the length of the third side of a triangle when two side lengths are already known, the Triangle Inequality Theorem can be applied.

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. Given side lengths of 7 cm and 4 cm, the third side must be greater than 3 cm (7 - 4) and less than 11 cm (7 + 4). Therefore, the correct answer to the question is C: The third side is longer than 3 cm and shorter than 11 cm.