Question

pam was told to draw a triangle with side lengths 3 centimeters, 5 centimeters, and 9 centimeters. complete the paragraph. since ( 3<5<9 ) and, pam draw a triangle with side lengths 3 centimeters, 5 centimeters, and 9 centimeters.

Explanation:

Step1: Apply triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\) (\(a\leq b\leq c\)), \(a + b>c\) must hold. Here \(a = 3\), \(b = 5\), \(c=9\). Calculate \(a + b\): \(3+5=8\).

Step2: Compare \(a + b\) and \(c\)

Since \(8<9\) (i.e., \(3 + 5<9\)).

Answer:

Since \(3<5<9\) and \(3 + 5<9\), Pam cannot draw a triangle with side lengths 3 centimeters, 5 centimeters, and 9 centimeters.