Question

a student is constructing a triangle with the following dimensions:

• side length of 10 inches
• side length of 30 inches

which measurements could be the length of the third side? choose two correct answers.
50 inches
19 inches
21 inches
45 inches
35 inches

Explanation:

Step1: Apply 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 \(a = 10\) and \(b=30\). Then \(|10 - 30|=20\) and \(10 + 30 = 40\). So \(20\lt c\lt40\).

Step2: Check each option

• For \(c = 50\): \(50\gt40\), so it does not satisfy \(20\lt c\lt40\).
• For \(c = 19\): \(19\lt20\), so it does not satisfy \(20\lt c\lt40\).
• For \(c = 21\): \(20\lt21\lt40\), so it satisfies the inequality.
• For \(c = 45\): \(45\gt40\), so it does not satisfy \(20\lt c\lt40\).
• For \(c = 35\): \(20\lt35\lt40\), so it satisfies the inequality.

Answer:

21 inches, 35 inches