1992 AMC 8 Problem 22
Attempt Problem 22 of the 1992 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 1992 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
Eight square tiles are arranged as shown so their outside edges form a polygon with a perimeter of units. Two additional tiles of the same size are added to the figure so that at least one side of each added tile is shared with a side of one of the squares in the original figure. Which of the following could be the perimeter of the new figure?
Small hint:
Adding a tile that shares exactly one side changes the perimeter by ; sharing two sides changes it by
Big hint:
With two added tiles, the total change can be or ; add these to
Solution:
A tile that shares exactly one side adds to the perimeter (four new edges minus two hidden), while a tile sharing two sides adds
With two added tiles the perimeter can change by or giving new perimeters of or Of the choices, only is possible.
Thus, the correct answer is C .
Problem 22 in other years
- 1985 AMC 8
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