2017 AMC 8 Problem 16
Attempt Problem 16 of the 2017 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 2017 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
16.
In the figure shown below, choose point on side so that and have equal perimeters. What is the area of
Answer: D
Small hint:
Use the equal-perimeter condition to find and .
Big hint:
Once is split, the two triangles have the same altitude from , so compare areas by base lengths.
Video solution:
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Written solution:
The only way to split into two parts such that the two triangles have the same perimeter is if and
and have the same altitudes, so their areas are proportional to their bases. This means that the area of is the area of which is
Thus, D is the correct answer.
Problem 16 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
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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- 2012 AMC 8
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