Four segments measure 16, 19, 43 and 50 centimeters. what is the probability that a triangle can be formed if three of these segments are chosen at random?

Question

Mathematics

Vivian Giles

1 March, 18:58

Four segments measure 16, 19, 43 and 50 centimeters. what is the probability that a triangle can be formed if three of these segments are chosen at random?

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Answers (1)

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Agustin Shea · Answer 1

OK, a triangle first of all needs to have a certain condition satisfied. The length of one side of a triangle can not equal the length of 2 sides combined. So in a triangle a + b = c, a + b can not be less than c (a + b ≮ c). Therefore, there are only a few possibilities that will work here. Let's find them:

16, 19, 43; no

16, 19, 50; no

16, 43, 50; yes

19, 43, 50; yes

Since only 2 out of 4 form triangles, there is a 50% chance you'll pick the right segments to form a triangle.