Question

1. the lengths of two sides of a triangle are shown.

57 and 16
complete the inequality to show the possible side
measures, x, that can be used to create a triangle
using the two given lengths.
__ < x < __

Explanation:

Step1: Recall Triangle Inequality Theorem

The triangle inequality theorem states that the length of any side of a triangle must be greater than the absolute difference of the other two sides and less than the sum of the other two sides. For two sides \(a\) and \(b\), the third side \(x\) must satisfy \(|a - b| < x < a + b\).

Step2: Identify \(a\) and \(b\)

Here, \(a = 57\) and \(b = 16\). First, calculate the absolute difference: \(|57 - 16| = |41| = 41\). Then, calculate the sum: \(57 + 16 = 73\).

Step3: Form the Inequality

Using the triangle inequality theorem, the inequality for \(x\) is \(41 < x < 73\). The original answer had an incorrect upper bound (59.2 instead of 73), likely a miscalculation. The correct bounds come from the sum and difference of the two given sides.

Answer:

\(41 < x < 73\)