2002 AMC 8 Problem 16
Attempt Problem 16 of the 2002 AMC 8 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 2002 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
16.
Right isosceles triangles are constructed on the sides of a right triangle, as shown. A capital letter represents the area of each triangle. Which one of the following is true?
Answer: E
Small hint:
Each right isosceles triangle has area half the square of the side it is built on.
Big hint:
Compute the areas on the sides and
Solution:
For a right isosceles triangle built on a side of length the two legs have length so its area is
These values satisfy and the other listed equations do not.
Thus, E is the correct answer.
Problem 16 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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