Question

Which of the following can be the perimeter of a triangle if one of its sides is 7776 units, the second side (say p) is a square of the perfect square of an integer number, and the third side (say q) is a power of 6. It is also known that q is six times of p.

• A. 16848 units
• B. 16832 units
• C. 16880 units
• D. 16874 units
• E. 16866 units

Answer 1

Answer: (A)

16848 units

Answer 2

Let the second side be $a^4$ units
Let the third side be $6x$ units.
Given that,
$a^4 \times 6 = 6^x$
or, $a^4 = 6^{x-1}$
Total perimeter $(P)$ = $7776 + a^4 + 6^x = 7776 + 6^{x-1} + 6^x = 7776 + 6^{x-1} \times 7$
$\Rightarrow p- 7776 = 6^{x-1} \times 7$
From the given options, only $16848 - 7776$ is divisible by $7$.

Hence, option A is the correct answer.