1989 AMC 12 Problem 17
Attempt Problem 17 of the 1989 AMC 12 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 1989 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
17.
The perimeter of an equilateral triangle exceeds the perimeter of a square by cm. The length of each side of the triangle exceeds the length of each side of the square by cm. The square has perimeter greater than How many positive integers are not possible values for
infinitely many
Answer: D
Small hint:
Let the square’s side length be
Big hint:
Translate the positive-perimeter condition into a strict inequality for
Solution:
If the square has side the triangle has side The perimeter condition gives so The condition is equivalent to Thus the positive integers through are precisely the impossible values.
Thus the correct answer is D.
Problem 17 in other years
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