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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Two of the three sides of a triangle are $20$ and $15.$ Which of the following numbers is not a possible perimeter of the triangle?

$52$

$57$

$62$

$67$

$72$

Answer: E

Concepts:triangle inequality bounding to limit cases

Difficulty rating: 1020

Small Hint:

The third side lies strictly between $20-15$ and $20+15$

Big Hint:

Add $20+15$ to that range to bound the perimeter

Solution:

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

The perimeter is $35 + s,$ so it lies strictly between $40$ and $70.$ Among the choices, only $72$ falls outside this range.

Thus, the correct answer is E.

Problem 1#1

Full Exam

Problem 3#3

Problem 2 in Other Years

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