1971 AMC 12 Problem 28
Attempt Problem 28 of the 1971 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 1971 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
Nine lines parallel to the base of a triangle divide the other sides each into equal segments and the area into distinct parts. If the area of the largest of these parts is then the area of the original triangle is:
Answer: C
Small hint:
The largest part is the bottom strip
Big hint:
The smaller triangle above that strip has linear scale
Solution:
If the whole area is the triangle above the bottom strip is similar to the original with scale so its area is Thus the largest strip has area giving
Therefore, the correct answer is C.
Problem 28 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
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- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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