Question

problem 7: (first taught in lesson 45) tell whether each set of numbers in the box below can represent the side lengths of a triangle. after you pick your answer press go. a. 5, 8, 14 yes no b. 12, 16, 20 yes no

Explanation:

Step1: Apply triangle inequality theorem

For a set of numbers \(a\), \(b\), \(c\) (where \(a\leq b\leq c\)) to be side lengths of a triangle, \(a + b>c\) must hold.

Part a:

Given \(a = 5\), \(b = 8\), \(c = 14\)
Check \(a + b>c\): \(5+8 = 13\)
Since \(13<14\) (i.e., \(5 + 8<14\)), the triangle - inequality theorem is not satisfied.

Part b:

Given \(a = 12\), \(b = 16\), \(c = 20\)
Check \(a + b>c\): \(12 + 16=28\)
Since \(28>20\) (i.e., \(12+16>20\)), also check other pairs: \(12 + 20>16\) (\(32>16\)) and \(16+20>12\) (\(36>12\))

Answer:

a. No
b. Yes