Consider the following triangle side lengths and determine if the triangle could exist. Justify your answer. Part A: 21,18,17 Part B: 3,12,8

A yes, B no

Step-by-step explanation:

The triangle inequality states that the sum of any 2 sides of the triangle must be greater than the third side.

A Given 21, 18, 17 , then

21 + 18 = 39 > 17

21 + 17 = 38 > 18

18 + 17 = 35 > 21

Thus the triangle could exist

B Given 3, 12, 8 , then

3 + 12 = 9 > 8

3 + 8 = 11 < 12 ← fails the test

Thus the triangle does not exist