2015 AMC 12A Problem 2

Attempt Problem 2 of the 2015 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2015 AMC 12A solutions, or check the answer key.

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2.

Two of the three sides of a triangle are 2020 and 15.15. Which of the following numbers is not a possible perimeter of the triangle?

5252

5757

6262

6767

7272

Answer: E
Concepts:triangle inequalitybounding to limit cases
Difficulty rating: 1020
Solution:

By the Triangle Inequality, the third side ss satisfies 2015<s<20+15,20-15 \lt s \lt 20+15, that is 5<s<35.5 \lt s \lt 35.

The perimeter is 35+s,35 + s, so it lies strictly between 4040 and 70.70. Among the choices, only 7272 falls outside this range.

Thus, the correct answer is E.

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