Final answer:
The lengths of the sides of a horizontal cross-section of a pyramid maintain the same ratio as the sides of the base, which means they are proportionally smaller as you move up the pyramid.
Step-by-step explanation:
The question pertains to the properties of a horizontal cross-section of a pyramid. By geometry principles, when you make a horizontal cross-section of a pyramid, the resulting shape is similar to the base but scaled down. Therefore, the lengths of the sides of the cross-section (they) are proportional to the sides of the base. This is because as you move up the pyramid, the cross-sections become smaller, but maintain the shape of the base. Hence, the correct answer to the question is:
C. They have the same ratio as the lengths of the sides of the base.
To illustrate this with an example, if the base is a square with side length of 4 units, a horizontal cross-section halfway up the pyramid might be a square with side lengths of 2 units. These numbers don't necessarily match the lengths of the base, but the ratio (1:2 in this example) between the cross-section's sides and the base's sides remains consistent.