Question

1. is it possible to construct a triangle with the given side lengths? justify your answer. 22, 26, 65

Explanation:

Step1: Recall the triangle inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check the sum of the two shorter sides

The two shorter sides are \(22\) and \(26\). Their sum is \(22 + 26=48\).

Step3: Compare with the longest side

The longest side is \(65\). Since \(48<65\), the triangle inequality theorem is violated.

Answer:

No, it is not possible to construct a triangle with side lengths \(22\), \(26\), and \(65\) because \(22 + 26 = 48<65\), which does not satisfy the triangle inequality theorem.