The sides of a triangle are three consecutive odd numbers. The sum of the lengths

The sides of a triangle are three consecutive odd numbers. The sum of the lengths of the sides of a triangle is 21. What are the sides?

As you know, any positive odd number n can be represented as n = 2 * k – 1, where k is a natural number. Suppose the numbers are 2 * k – 1; 2 * k + 1 and 2 * k + 3 are the required three consecutive odd numbers.
Then, according to the condition of the task, the sum of the lengths of the sides of the triangle is 21, that is, 2 * k – 1 + 2 * k + 1 + 2 * k + 3 = 21 or 6 * k + 3 = 21, whence k = (21 – 3): 6 = 18: 6 = 3.
Thus, we have found 3 consecutive odd numbers 5; 7 and 9. The task states that these numbers are the sides of a triangle. There are certain conditions for the existence of a triangle, for example, the semi-perimeter of a triangle is greater than any of its sides. For the numbers we found, the semiperimeter is (5 + 7 + 9): 2 = 21: 2 = 10.5. Obviously, the above condition is fulfilled.
Answer: 5, 7, 9.