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.
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.
Updated On: Jan 27, 2024
- 16848 units
- 16832 units
- 16880 units
- 16874 units
- 16866 units
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The Correct Option is A
Solution and Explanation
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.
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