Question

question 5 1 pts two sides of a triangle measure 20 and 55 units. between what two measures can the third side be? < length of third side <

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 \(c\) satisfies \(|a - b| < c < a + b\).

Step2: Identify the given sides

Here, the two sides are \(a = 55\) and \(b = 20\).

Step3: Calculate the difference

First, find the absolute difference: \(|55 - 20| = |35| = 35\).

Step4: Calculate the sum

Next, find the sum: \(55 + 20 = 75\).

Answer:

\(35 < \text{length of third side} < 75\)