1998 AMC 12 Problem 15
Attempt Problem 15 of the 1998 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 1998 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
15.
A regular hexagon and an equilateral triangle have equal areas. What is the ratio of the length of a side of the triangle to the length of a side of the hexagon?
Answer: C
Small hint:
Partition the regular hexagon into six equilateral triangles
Big hint:
Equilateral-triangle area is proportional to the square of its side
Solution:
A regular hexagon of side is six equilateral triangles of side An equal-area equilateral triangle of side therefore satisfies so The correct answer is C.
Problem 15 in other years
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