See
https://learn1.open.ac.uk/mod/oublog/viewpost.php?post=258608for the problem,.
Solution
Suppose the origins equilateral triangle has sides of length 1. Then its three vertices are each 1 unit from the other two.
If we tried to cover it with two other triangles, then one of them would have to cover two vertices of the original triangle, because there are three vertices distributed between two covering triangles. So at least one of the covering triangles would have to contain points 1 unit apart, so it couldn’t be smaller than the original triangle.