The maximum possible side length of the base of the building is; C: 71 feet.
The given parameters of the new building in the shape of a square pyramid that is to be constructed are as follows:
Base is expressed as b
Slant height (l) is expressed as 5b
The lateral surface area of the square pyramid is calculated from the formula given as;
LSA = 2bl
Thus, the lateral surface area is expressed as;
L = 2 * b * 5b
L = 10b²
The total surface area is calculated using the formula:
T = L + b²
Thus, plugging in the value of 10b² for L gives the total surface area as;
T = 10b² + b²
T = 11b²
The maximum surface area is 50,000 square feet and so we can find b from the following expression;
11b² = 50000
Divide both sides of the equation by 11 to get;
b² = 50000/11
b = √(50000/11)
b = 71 feet to the nearest foot.
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