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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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

The third side lies strictly between

20-15

and

20+15

Add

20+15

to that range to bound the perimeter

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 2 in other years