The probability of the grain of sand landing on the portion of the base outside the triangle is 3/4. Hence, The probability of the grain of sand landing on the portion of the base inside the triangle is (1 - 3/4) = 1/4.

Therefore, the ratio of area of the triangle to the area of the base of the cylinder = 1/4

Say, length of each side of the equilateral triangle is a.
Hence, area of the equilateral triangle = (√3/4)*a²

Now, circumference of the base = 4√(π√3)
So, the radius of the base = 4√(π√3)/(2π)
So, area of the base = π[4√(π√3)/(2π)]² = π[16*(π√3)/(4π²)] = 4√3

Hence, area of the equilateral triangle = √3

Hence, (√3/4)*a² = √3 ---> a = √4 = 2

The correct answer is E.