1964 AMC 12 Problem 10
Attempt Problem 10 of the 1964 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 1964 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
10.
Given a square with side of length On a diagonal as base a triangle with three unequal sides is constructed so that its area equals that of the square. The length of the altitude drawn to the base is:
Answer: A
Small hint:
The square’s diagonal has length
Big hint:
Set
Solution:
The triangle’s base is the square’s diagonal, If its altitude is equality of areas gives so
Therefore, the correct answer is A.
Problem 10 in other years
- 1950 AMC 12
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