Graduate Management Admission Test (GMAT) Practice Test

How many smaller triangles can an equilateral triangle be divided into equally?

1. 1

2. 2

3. 3

4. 4

The correct answer is: 3

An equilateral triangle can be divided into smaller triangles in several ways, but a common and straightforward method involves splitting it into three smaller triangles of equal area. This is achieved by connecting each vertex of the triangle to the midpoint of the opposite side. When this is done, each corner of the triangle forms a vertex of a smaller triangle, creating three identical triangles within the original equilateral triangle. This division preserves the properties of the original triangle, ensuring that all smaller triangles created are also equilateral and congruent to one another. Each of these smaller triangles has the same area as well, maintaining equality among them. Therefore, the correct answer reflects the number of equally sized smaller triangles that can be produced from an equilateral triangle through this effective method of division.