Final answer:
To find the maximum side length of the base of a square pyramid where the slant height is five times the base side length, calculate the surface area with the upper limit of the construction material. Solving for side length yields approximately 67 feet, which must be rounded if to the nearest foot. The options presented in the question do not include this calculation, which could indicate a mistake in the provided choices.
Step-by-step explanation:
To determine the maximum possible side length of the base of the building, we need to consider the surface area of the pyramid, which includes the base area and the area of the four triangular faces. The side length of the base is s, the slant height is 5s (since it's five times the side length of the base), and the construction material to be used for the outside of the building will be between 20,000 and 50,000 square feet.
The surface area (SA) of a square pyramid can be calculated using the formula: SA = base area + (perimeter of the base * slant height) / 2. For a square base, the base area is s² and the perimeter is 4s. Thus, SA = s² + (4s * 5s) / 2 = s² + 10s² = 11s².
To find the maximum side length, set the upper limit of the construction material (50,000 square feet) to the calculated surface area of the pyramid: 50,000 = 11s². Solving for s, we get s² = 4545.4545 and s = 67.42 feet. Since we need to round to the nearest foot, we get 67 feet as the maximum possible side length. None of the provided options match this calculation, so we must assume there is a typo in the question, and the correct maximum side length is not listed.