Question

a triangle has two sides of length 10 cm and 14 cm. what can you say about the length of the third side? choose the correct answer below. a. the third side must be less than 140 cm. b. the third side must be greater than 24 cm and less than 140 cm. c. the third side must be greater than 4 cm. d. the third side must be less than 24 cm and greater than 4 cm.

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side, and the difference between the lengths of any two sides must be less than the length of the third side.
Let the sides of the triangle be \(a = 10\) cm, \(b = 14\) cm, and \(c\) be the third - side.

1. First, consider \(a + b>c\), so \(10 + 14>c\), which simplifies to \(c<24\) cm.
2. Second, consider \(|a - b|

Answer:

D. The third side must be less than 24 cm and greater than 4 cm.