19) How many equilateral triangles are present in this figure?

(A) 16

(B) 20

(C) 25

(D) 26

(E) 27

![](https://cdn.mathpix.com/cropped/2024_04_17_b5d519ff6c1a8005abb1g-2.jpg?height=201&width=224&top_left_y=1697&top_left_x=1186)
19) The answer is $(E)$.

We set the side of the smallest triangles equal to 1. For each equilateral triangle, we simply call the vertex opposite to its horizontal side the vertex of the triangle. Then there are:

- 16 triangles of side 1 (10 with the vertex at the top and 6 with the vertex at the bottom);
- 7 equilateral triangles of side 2, of which 6 with the vertex at the top and 1 with the vertex at the bottom (the midpoint of the bottom side of the figure);
- 3 equilateral triangles of side 3 (all with the vertex at the top);
- 1 equilateral triangle of side 4 (the frame of the entire figure).