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Question:

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 397 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.

Explanation:

Let AB = a³ and AC = 3ⁿ

Also

AC = 3 × AB

∴ 3ⁿ = 3 × a³

∴ 3^{(n – 1)} = a³

Now, let the perimeter be equal to p

p = BC + AC + AB

= 397 + 3ⁿ + 3^{(n – 1)}

(p – 397) = 3^{(n – 1)} × (3 + 1)

= 3^{(n – 1)} × 4

Thus the LHS of the above equation should be a multiple of 3 and 4. Substitute the value of perimeter given in the options and verify this. Among the options, only (3313 – 397) is divisible by 3 and 4..

Hence, option (d).