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Quote:
In triangle ABC, side AB = 3 and side BC = 8. Which of the following CANNOT be the perimeter of triangle ABC?
Step 1: Understanding the question
When two sides of a triangle is given, then the third side lies between difference and sum of the two given sides
8-3 < Third side < 8+3
5 < Third side < 11

Possible range of perimeter is:
3+8+5 < Perimeter < 3+8+11
16 < Perimeter < 22

E is correct
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Bunuel
In triangle ABC, side AB = 3 and side BC = 8. Which of the following CANNOT be the perimeter of triangle ABC?

A 18
B 19
C 20
D 21
E 22
Solution:

Recall that the length of the longest side of a triangle is less than the sum of the lengths of the two shorter sides. Therefore, if AC is the longest side of triangle ABC, then AC < 3 + 8 = 11, and the perimeter of triangle ABC must be less than 3 + 8 + 11 = 22. Since the perimeter is less than 22, it can’t be 22.

Answer: E
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