1965 AMC 12 Problem 8
Attempt Problem 8 of the 1965 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 1965 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
8.
One side of a given triangle is inches. Inside the triangle a line segment is drawn parallel to this side forming a trapezoid whose area is one-third of that of the triangle. The length of this segment, in inches, is:
Answer: A
Small hint:
The smaller triangle above the segment has two-thirds of the original area
Big hint:
Linear scale factors are square roots of area scale factors
Solution:
The trapezoid occupies one third of the area, so the smaller similar triangle occupies two thirds. Its linear scale factor is Hence the parallel segment has length
Therefore, the correct answer is A.
Problem 8 in other years
- 1950 AMC 12
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