2003 AMC 10A Problem 7

Attempt Problem 7 of the 2003 AMC 10A 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 2003 AMC 10A solutions, or check the answer key.

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7.

How many non-congruent triangles with perimeter 77 have integer side lengths?

11

22

33

44

55

Answer: B
Concepts:triangle inequalitysystematic listing
Difficulty rating: 1250
Solution:

The longest side cannot exceed 3,3, since otherwise the other two sides could not reach it.

The only possibilities are side lengths 11-33-33 and 22-22-3,3, giving 22 triangles.

Thus, the correct answer is B.

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