A triangle having all sides of different lengths is called :

Question

Accepted Answer

A triangle having all sides of different lengths is called a scalene triangle. Let's explore why Option 1 is the correct answer and why the other options are incorrect:

1. **Scalene Triangle (Option 1):** A scalene triangle is defined as a triangle in which all three sides have different lengths. This means that no two sides are equal, and consequently, all three angles are also different. This definition perfectly matches the description given in the question, making Option 1 the correct answer.

2. **Right Triangle (Option 2):** A right triangle is characterized by having one angle that is exactly 90 degrees. While a right triangle can have sides of different lengths, the defining feature is the right angle, not the differing side lengths. Therefore, a right triangle does not necessarily have all sides of different lengths, and this option does not specifically address the question's requirement.

3. **Equilateral Triangle (Option 3):** An equilateral triangle has all three sides of equal length, and all three angles are equal, each measuring 60 degrees. This is the opposite of what the question describes, as an equilateral triangle does not have sides of different lengths. Thus, Option 3 is incorrect.

4. **Isosceles Triangle (Option 4):** An isosceles triangle has at least two sides that are equal in length. This means that it does not meet the condition of having all sides of different lengths. Therefore, Option 4 does not satisfy the criteria given in the question.

In conclusion, the only option that accurately describes a triangle with all sides of different lengths is a scalene triangle, making Option 1 the correct answer.