2015 AMC 8 Problem 25
Attempt Problem 25 of the 2015 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2015 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
25.
One-inch squares are cut from the corners of this inch square. What is the area in square inches of the largest square that can be fitted into the remaining space?
Answer: C
Small hint:
The fitted square can be tilted around the central square.
Big hint:
Add the central square area and the four congruent corner triangles.
Video solution:
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Written solution:
For a largest fitted square, each side must touch an inner corner of one of the removed -inch squares; otherwise the fitted square could be enlarged. Thus it surrounds the central square and adds four congruent right triangles, one along each side.
The central square has area Each added triangle has base and height so the four triangles have total area
The fitted square has area
Thus, C is the correct answer.
Problem 25 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
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- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
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