There is a triangular building (ABC) located in the heart of Jaipur, the Pink City. The length of the one wall in east (BC) direction is 1500 feet. If the length of south wall (AB) is perfect cube, the length of southwest wall (AC) is a power of three, and the length of wall in southwest (AC) is thrice the length of side AB, determine the perimeter of this triangular building.
Now, $$3^n, 3^{n+1}$$ pairs are (1,3), (27,81), (729, 2187) and so on 1500, 3 and 397 cannot form a triangle 1500, 81 and 397 cannot form triangle 1500, 729 and 2187 can form a triangle Thus, the perimeter of the building = 1500+729+2187 = 4416 feet Hence, option D is the correct answer.
