Final answer:
In geometry, an intersecting plane can theoretically have an infinite number of sides. For the perpendicular component of a box's weight on an inclined plane, the maximum is reached at a 90° incline when the full weight acts perpendicularly to the plane.
Step-by-step explanation:
The question regarding the maximum number of sides an intersecting plane can have delves into the concept of geometry. When a plane intersects a three-dimensional shape, such as a polyhedron, the intersection is a two-dimensional figure. The maximum number of sides this figure can have is theoretically infinite if the intersecting plane cuts through an infinite number of faces, as would be the case with certain complex shapes or theoretically with a shape like a cylinder. Therefore, the answer is d) Infinite.
Now, let's delve into the second part of the question related to the perpendicular component of a box's weight on an inclined plane. The perpendicular component of weight on an inclined plane is at its maximum when the incline angle is 90° because it is equivalent to the full weight of the box acting directly downwards due to gravity, with no component being parallel to the plane at this angle. So the correct answer is d) 90°.