Question

two sides of a triangle measure 5 in. and 12 in. which could be the length of the third side? 18 in. 6 in. 10 in. 3 in.

Explanation:

Step1: Apply the triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following must hold: \(|a - b|\lt c\lt a + b\). Let \(a = 5\) and \(b=12\). Then \(|5 - 12|=7\) and \(5 + 12 = 17\). So \(7\lt c\lt17\).

Step2: Check each option

• For \(c = 18\): \(18>17\), so it does not satisfy the inequality.
• For \(c = 6\): \(6<7\), so it does not satisfy the inequality.
• For \(c = 10\): \(7<10<17\), so it satisfies the inequality.
• For \(c = 3\): \(3<7\), so it does not satisfy the inequality.

Answer:

10 in.