Question

question 35 of 50
a triangle cannot have side lengths that are 3, 5, and 9.
∘ false
∘ true

Explanation:

Step1: Recall Triangle Inequality

For a triangle with sides \(a\), \(b\), \(c\), the sum of any two sides must be greater than the third side. So we check \(3 + 5\), \(3 + 9\), and \(5 + 9\) against the third side.

Step2: Check \(3 + 5\)

Calculate \(3 + 5 = 8\). Now, compare with the third side \(9\). Since \(8 < 9\), the sum of two sides (\(3\) and \(5\)) is not greater than the third side (\(9\)). This violates the triangle inequality theorem.

Step3: Conclusion

Since the side lengths \(3\), \(5\), and \(9\) do not satisfy the triangle inequality, a triangle cannot have these side lengths. So the statement is True.

Answer:

True