Question

two sides of a triangle measure 8 cm and 15 cm. which could be the length of the third side? 18 cm 24 cm 28 cm 6 cm

Explanation:

Step1: Apply triangle - inequality theorem

The triangle - inequality theorem states that for a triangle with side lengths \(a\), \(b\), and \(c\), the following inequalities must hold: \(|a - b|\lt c\lt a + b\). Let \(a = 8\) and \(b = 15\). Then \(|8 - 15|=7\) and \(8 + 15 = 23\). So \(7\lt c\lt23\).

Step2: Check each option

• For \(c = 18\): Since \(7\lt18\lt23\), this satisfies the triangle - inequality theorem.
• For \(c = 24\): Since \(24\gt23\), this does not satisfy the triangle - inequality theorem.
• For \(c = 28\): Since \(28\gt23\), this does not satisfy the triangle - inequality theorem.
• For \(c = 6\): Since \(6\lt7\), this does not satisfy the triangle - inequality theorem.

Answer:

18 cm