1954 AMC 12 Problem 29
Attempt Problem 29 of the 1954 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 1954 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
29.
If the ratio of the legs of a right triangle is then the ratio of the corresponding segments of the hypotenuse made by a perpendicular upon it from the vertex is:
Answer: A
Small hint:
The two hypotenuse segments are the projections of the legs
Big hint:
By similarity, their ratio is the ratio of the squares of the corresponding legs
Solution:
If the legs have lengths and their projections on the hypotenuse have lengths and Their ratio is therefore With this is
Thus, the correct answer is A.
Problem 29 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
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