5. (10 points) As shown in the figure, there are 10 nails on a wooden board, and the distance between any two adjacent nails is equal. Using these nails as vertices, the number of equilateral triangles that can be formed with rubber bands is:
Pick one
Solution
【Analysis】
Connect as shown in the above figure, count the single triangles, the large triangles composed of 4 triangles, and the largest triangle on the outside, in three categories;
【Solution】Solution: There are 9 single triangles,
3 large triangles composed of 4 triangles,
1 largest triangle on the outside,
In total: (triangles)
Answer: 13 equilateral triangles can be formed using rubber bands.
Therefore, the correct choice is: .
Want a route through all this instead of an archive? The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.