Which of the following triangles is a scalene triangle?

• A. A triangle with side lengths $1$, $1$, and $1$
• B. A triangle with side lengths $2$, $2$, and $3$
• C. A triangle with side lengths $3$, $4$, and $5$
• D.

Answer: (C)

Verified step by step guidance

1. Recall the definition of a scalene triangle: it is a triangle where all three sides have different lengths.
2. Examine the first triangle with side lengths 1, 1, and 1. Since all sides are equal, this is an equilateral triangle, not scalene.
3. Look at the second triangle with side lengths 2, 2, and 3. Here, two sides are equal, so this is an isosceles triangle, not scalene.
4. Consider the third triangle with side lengths 3, 4, and 5. All three sides have different lengths, which fits the definition of a scalene triangle.
5. Therefore, the triangle with side lengths 3, 4, and 5 is the scalene triangle among the options.