2019 AMC 8 Problem 21
Attempt Problem 21 of the 2019 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 2019 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
What is the area of the triangle formed by the lines and
Answer: E
Small hint:
Find the three pairwise intersections
Big hint:
Use the horizontal side on as the base
Video solution:
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Written solution:
First, let us find the vertices of the triangle. The intersections between and the other two lines are and .
To find the third intersection, we can equate the two equations to get
This gives us the point
Note that the first two intersection points are mirrored across the -axis. This tells us that the triangle is isosceles.
The base is therefore and the height is The area of the triangle is therefore
Thus, the correct answer is E.
Problem 21 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
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