An equilateral triangular plate is to be cut into n number of identical small equilateral triangular plates. Which one of the following can be possible value of n ?

A standard subdivision of an equilateral triangle is obtained by dividing each side into m equal segments and drawing parallels to the sides; this produces m^2 congruent small equilateral triangles, so any achievable n must be a perfect square . More generally, results on triangle subdivision state that if N is a perfect square then the triangle can be partitioned into N congruent triangles . Among the given choices, 256 = 16^2 is a perfect square (and hence a valid value for n); note that 196 = 14^2 is also a perfect square, so it too would be possible, but 256 is explicitly one of the options that satisfies the necessary condition of being a square .