The given information states that the diagonals of a rhombus are in the ratio 3:4 and the area of the rhombus is 2400 cm^2. We need to find the length of the side of the rhombus.

Let's consider the diagonals of the rhombus. Let the length of the shorter diagonal be 3x and the length of the longer diagonal be 4x.

We know that the area of a rhombus is given by the formula: A = (d1*d2)/2, where d1 and d2 are the lengths of the diagonals.

Substituting the given values, we have: 2400 = (3x*4x)/2
Simplifying further, we get: 2400 = 6x^2

Dividing both sides of the equation by 6, we have: 400 = x^2

Taking the square root of both sides, we get: √400 = x
Therefore, x = 20

Now that we know the value of x, we can find the length of the side of the rhombus.

The diagonals of a rhombus bisect each other at right angles, dividing the rhombus into four congruent right-angled triangles. Each of these triangles has a base equal to half the length of the shorter diagonal (3x/2) and a height equal to half the length of the longer diagonal (4x/2).

Using the formula for the area of a triangle (A = (1/2) * base * height), we can calculate the area of one of these triangles and then multiply it by 4 to find the total area of the rhombus.

Area of one triangle = (1/2) * (3x/2) * (4x/2) = (3x^2)/4

Total area of the rhombus = 4 * (3x^2)/4 = 3x^2

Substituting the value of x, we get: Total area = 3 * (20^2) = 3 * 400 = 1200 cm^2

However, the given area of the rhombus is 2400 cm^2. It appears that there is a contradiction in the given information, as the calculated area does not match the given area.

Therefore, it is not possible to determine the length of the side of the rhombus based on the given information.