Question

unit 6 quiz
you may use your notes to complete this quiz. it may be taken two times.
1 multiple choice 5 points
the lengths of two sides of a triangle are 26 meters and 48 meters.
what is the range of possible lengths, in meters, for the third side, x, of the triangle? write an inequality.
26 < x < 74
x > 48
26 < x < 48
22 < x < 74

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 a triangle with sides \(a\), \(b\), and \(x\), we have \(|a - b| < x < a + b\).

Step2: Identify the given sides

Here, the two given sides are \(a = 26\) meters and \(b = 48\) meters.

Step3: Calculate the difference and sum

First, find the difference: \(|48 - 26| = 22\). Then, find the sum: \(48 + 26 = 74\).

Step4: Apply the inequality

Using the triangle inequality theorem, the length of the third side \(x\) must satisfy \(22 < x < 74\).

Answer:

\(22 < x < 74\) (corresponding to the option "22 < x < 74")