2003 AMC 12B Problem 10
Attempt Problem 10 of the 2003 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 2003 AMC 12B solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
10.
Several figures can be made by attaching two equilateral triangles to the regular pentagon in two of the five positions shown. How many non-congruent figures can be constructed in this way?
Small hint:
By symmetry, assume one triangle is attached to a fixed side, then place the second
Big hint:
Only the two sides adjacent versus non-adjacent to the fixed side give different shapes, up to reflection
Solution:
Assume one triangle is attached to side The second triangle can be attached to a side that is one step away or two steps away from
Attaching it to or gives two figures; attaching it to or gives figures that are mirror images of these across the pentagon’s axis of symmetry.
So there are only non-congruent figures.
Thus, the correct answer is B.
Problem 10 in other years
- 1950 AMC 12
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