Question

assignment 8.2: triangle inequality theorem
determine whether a triangle can be formed by the following side lengths.

1. 9 in., 12 in., and 18 in.
2. 29 m, 59 m, and 89 m

Explanation:

Step1: Triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (\(c\geq a,c\geq b\)), the triangle inequality theorem states \(a + b>c\)

Step2: Check problem 7

Let \(a = 9\), \(b=12\), \(c = 18\). Then \(a + b=9 + 12=21\), and \(21>18\)

Step3: Check problem 8

Let \(a = 29\), \(b = 59\), \(c=89\). Then \(a + b=29+59 = 88\), and \(88<89\)

Answer:

1. Yes
2. No