2004 AMC 8 Problem 24
Attempt Problem 24 of the 2004 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 2004 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
24.
In the figure, is a rectangle and is a parallelogram. Using the measurements given in the figure, what is the length of the segment that is perpendicular to and
Answer: C
Small hint:
Find the area of the rectangle and subtract the four corner triangles.
Big hint:
Use the Pythagorean theorem to get the parallelogram base
Solution:
The rectangle has side lengths and so its area is
The four corner triangles have total area Thus parallelogram has area
Segment has length by the right triangle. Since the parallelogram area is we have so
Thus, C is the correct answer.
Problem 24 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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