Question 107

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.

Solution

The given condition is as shown below:-


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.

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