Question

1. is it possible to construct a triangle with the given side lengths? justify your answer. 6, 43, 39

Explanation:

Step1: Check triangle inequality

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), the triangle inequality is \(a + b>c\). Here \(a = 6\), \(b = 39\), \(c = 43\).
Calculate \(a + b\): \(6+39=45\)

Step2: Compare with \(c\)

Since \(45>43\) (i.e., \(a + b>c\))

Answer:

Yes, it is possible to construct a triangle with side lengths \(6\), \(39\), \(43\) because the sum of the two shorter sides (\(6 + 39\)) is greater than the longest side (\(43\)) which satisfies the triangle - inequality theorem.