1992 AMC 8 Problem 17

Attempt Problem 17 of the 1992 AMC 8 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 1992 AMC 8 solutions, or check the answer key.

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

17.

The sides of a triangle have lengths 6.5,6.5, 10,10, and s,s, where ss is a whole number. What is the smallest possible value of s?s?

33

44

55

66

77

Answer: B
Concepts:triangle inequality

Difficulty rating: 960

Solution:

By the triangle inequality, 6.5+s6.5 + s must exceed the longest side 10,10, so s>3.5.s \gt 3.5.

The smallest whole number greater than 3.53.5 is 4,4, and it does form a valid triangle.

Thus, the correct answer is B .

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