1953 AMC 12 Problem 26
Attempt Problem 26 of the 1953 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 1953 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
26.
The base of a triangle is inches. Two lines are drawn parallel to the base, terminating in the other two sides, and dividing the triangle into three equal areas. The length of the parallel closer to the base is:
inches
inches
inches
inches
none of these
Answer: A
Small hint:
The triangle above the lower parallel contains two-thirds of the total area
Big hint:
For similar triangles, the area ratio is the square of the corresponding-length ratio
Solution:
The parallel closer to the base bounds a smaller triangle above it whose area is of the whole triangle. If its length is similarity gives Hence and
Thus, the correct answer is A.
Problem 26 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
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