Question

multiple answer 5 points select all possible side lengths of a triangle if two of the side lengths are 24 ft and 46 ft. 22 24 68 42 71 13 previous

Explanation:

Step1: Recall triangle inequality theorem

The triangle inequality theorem states that for a triangle with side lengths \(a\), \(b\), and \(c\), the sum of any two sides must be greater than the third side, and the difference of any two sides must be less than the third side. Let the third side be \(x\). Given two sides \(a = 24\) ft and \(b=46\) ft. Then we have two inequalities: \(|a - b| < x < a + b\).

Step2: Calculate the bounds

First, calculate \(|24 - 46|=| - 22| = 22\) and \(24 + 46=70\). So the third side \(x\) must satisfy \(22 < x < 70\).

Step3: Check each option

• For \(22\): \(22\) is not greater than \(22\) (since \(x>22\)), so it's not valid.
• For \(24\): \(22<24 < 70\), so it's valid.
• For \(68\): \(22<68 < 70\), so it's valid.
• For \(42\): \(22<42 < 70\), so it's valid.
• For \(71\): \(71\) is not less than \(70\) (since \(x < 70\)), so it's not valid.
• For \(13\): \(13\) is not greater than \(22\) (since \(x>22\)), so it's not valid.

Answer:

24, 42, 68 (the options corresponding to these values: 24, 42, 68)