In order for a triangle to be valid, the sum of the lengths of any two sides must be greater than the length of the remaining side. Let's check if this condition is met for the given lengths of 34, 23, and 12:
34 + 23 > 12 - Condition met
34 + 12 > 23 - Condition met
23 + 12 > 34 - Condition met
Since all three conditions are met, the given lengths can form a valid triangle. To determine the type of triangle, we can compare the lengths of the sides:
The length of all sides is different, so it is not an equilateral triangle.
No two sides have the same length, so it is not an isosceles triangle.
The sum of the squares of the two shorter sides (12^2 + 23^2) is less than the square of the longest side (34^2), so it is not a right triangle.
Therefore, the given triangle with side lengths 34, 23, and 12 is a scalene triangle, which means that all three sides have different lengths.