When the distributed loading acts perpendicular to an area, its intensity varies linearly for the determination of moment of inertia about the inclined axis. This can be explained by considering the definition of moment of inertia and the nature of the distributed loading.

Moment of inertia is a measure of an object's resistance to changes in rotational motion. It depends on the mass distribution of the object and the axis of rotation. For an area, the moment of inertia is calculated by integrating the product of the infinitesimal area and the square of its distance from the axis of rotation.

In the case of a distributed loading acting perpendicular to an area, the intensity of the loading can be represented by a linear equation. This means that the loading per unit area is constant throughout the area. The linear nature of the loading implies that the force acting on each infinitesimal area element is directly proportional to its distance from the axis of rotation.

The moment of inertia is determined by summing the contributions from all the infinitesimal area elements. Since the loading intensity varies linearly, the force acting on each element can be expressed as a linear function of its distance from the axis. When this linear variation is integrated over the entire area, the resulting moment of inertia will also have a linear variation with respect to the axis of rotation.

This linear variation of the moment of inertia is useful for calculations involving inclined axes. It simplifies the integration process and allows for easier determination of the moment of inertia. In contrast, if the loading intensity varied non-linearly, parabolically, or cubically, the integration process would be more complex and the determination of the moment of inertia would be more difficult.

Therefore, the correct answer is option 'A' - linearly. The linear variation of the loading intensity allows for a linear variation of the moment of inertia about the inclined axis, simplifying calculations and analysis.