Triangle Classification: Is a 10-10-7 Triangle Scalene?

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

To determine if the given triangle is a scalene triangle, we examine the side lengths $10$, $10$, and $7$.

A triangle is classified as scalene if all three side lengths are different. Therefore, we need to check the equality between any pairs of the given side lengths:

• Check if $10 = 10$: Yes, they are equal.
• Check if $10 = 7$: No, they are not equal.
• Check if $7 = 10$: No, they are not equal.

Since the triangle has two sides of equal length ($10$ and $10$), it does not satisfy the condition for being a scalene triangle.

In conclusion, the triangle is not a scalene triangle because two of its sides are equal.

Therefore, the solution to the problem is No.