2008 AMC 8 Problem 23
Attempt Problem 23 of the 2008 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 2008 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
23.
In square and What is the ratio of the area of to the area of square
Answer: C
Small hint:
Because only a ratio is needed, choose a convenient side length for the square.
Big hint:
Take the side length as so the split lengths are and
Solution:
Because the answer is a ratio, choose the side length of the square to be . Then , , , and .
The square has area . The areas of triangles and are each .
Triangle has area .
So , and the desired ratio is .
Thus, C is the correct answer.
Problem 23 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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