2022 AMC 12A Problem 3
Attempt Problem 3 of the 2022 AMC 12A 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 2022 AMC 12A solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
3.
Five rectangles, and are arranged in a square as shown below. These rectangles have dimensions and respectively. (The figure is not drawn to scale.) Which of the five rectangles is the shaded one in the middle?
Small hint:
The five areas add to the square’s area, which fixes the side length
Big hint:
Anchor the large and pieces in corners, then fit the rest
Solution:
The five areas are and which sum to So the square is
Placing () across the top left, () up the right side, () in the lower left, and () along the bottom leaves a central gap, which is exactly rectangle
Thus, the correct answer is B.
Problem 3 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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