Math problem of the day

Question:
The side length of an equilateral triangle is an integer. Which of the following could be its perimeter?

Answers variants: A. 123   B. 234   C. 345   D. No right answer   E. All of the above


Correct answer: E. All of the above
Tutorial:

The perimeter of an equilateral triangle is given by the formula P = 3*a, where a is the length common to all sides. Therefore, a = P/3, and a triangle has integral side length if and only if the perimeter is divisible by 3.
Furthermore, a number is divisible by 3 if and only if the sum of its digits is. We may implement this rule as many times as necessary to check divisibility, as follows.
123 is divisible by 3 because 1 + 2 + 3 = 6 and 6/3 = 2.
So is 234 because 2 + 3 + 4 = 9 and 9/9 = 3.
Lastly, so is 345 since 3 + 4 + 5 = 12, 1 + 2 = 3, and 3/3 = 1.
Since (A), (B) and (C) are valid, the correct answer is (D): All of the above.

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