2016 AMC 12B Problem 9
Attempt Problem 9 of the 2016 AMC 12B 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 2016 AMC 12B solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
9.
Carl decided to fence in his rectangular garden. He bought fence posts, placed one on each of the four corners, and spaced out the rest evenly along the edges of the garden, leaving exactly yards between neighboring posts. The longer side of his garden, including the corners, has twice as many posts as the shorter side, including the corners. What is the area, in square yards, of Carl’s garden?
Answer: B
Small hint:
Let the shorter side have posts and the longer side posts; the four corner posts are shared
Big hint:
Total posts a side with posts spans yards
Solution:
Let the shorter side have posts, so the longer side has Counting all posts and subtracting the four corners counted twice, giving The shorter side has posts, or yards, and the longer side has posts, or yards. The area is
Thus, the correct answer is B.
Problem 9 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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