Triangle Side Analysis: Is 41-42-36 a Scalene Triangle?

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

To determine if the triangle is scalene, we need to check if all sides are different and if they satisfy the triangle inequality theorem.

• Step 1: Verify all sides are different:
  Check $41 \neq 36$, $36 \neq 42$, and $41 \neq 42$. All statements are true, indicating all sides have different lengths.
• Step 2: Check the triangle inequality theorem:
  Evaluate:
  • $41 + 36 = 77 > 42$
  • $41 + 42 = 83 > 36$
  • $36 + 42 = 78 > 41$
  All inequalities are satisfied, confirming it forms a valid triangle.

Since the triangle has all different side lengths and satisfies the triangle inequality, it is indeed a scalene triangle.

Therefore, the solution to the problem is to conclude that the triangle is scalene.

The correct choice is $\text{Yes}$.