Triangle Side Analysis: Determining if a, 2a-a, and 3a Form a Scalene Triangle

Given the values of the sides of a triangle, is it a triangle with different sides?

To determine the type of triangle based on the given side lengths, we proceed as follows:

• Simplify the expressions for the side lengths:
• The first side is $a$.
• The second side simplifies as $2a-a = a$.
• The third side is $3a$.
• Compare the lengths to determine equality:
• The first side is $a$, and the second side is also $a$.
• The third side is $3a$, which is different from the first two sides ($a$).

Since the sides $a$, $a$, and $3a$ have two sides that are equal, the triangle is not a scalene triangle, which has all sides of different lengths.

Therefore, the triangle is not a triangle with different sides (scalene triangle). The correct answer is "No".