1983 AMC 12 Problem 28
Attempt Problem 28 of the 1983 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 1983 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
Triangle in the figure has area Points and all distinct from and are on sides and respectively, and If triangle and quadrilateral have equal areas, then that area is
not uniquely determined
Answer: C
Small hint:
Draw and cancel the common triangle from the equal areas
Big hint:
Equal areas of and imply ; then compare triangles and
Solution:
Draw From equality implies Their common base then gives so triangles and are similar. Hence Triangles and share the altitude from to so
Therefore, the correct answer is C.
Problem 28 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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- 1958 AMC 12
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