Given a triangle with side lengths $10$ in., $12$ in., and $15$ in., which classification best describes this triangle?

• A. Equilateral triangle
• B. Right triangle
• C. Scalene triangle
• D. Isosceles triangle

Answer: (C)

Verified step by step guidance

1. Identify the given side lengths of the triangle: 10 inches, 12 inches, and 15 inches.
2. Recall the definitions of triangle classifications based on side lengths: an equilateral triangle has all sides equal, an isosceles triangle has exactly two sides equal, and a scalene triangle has all sides of different lengths.
3. Compare the given side lengths to check for equality: since 10, 12, and 15 are all different, the triangle cannot be equilateral or isosceles.
4. To check if the triangle is a right triangle, apply the Pythagorean theorem by testing if the square of the longest side equals the sum of the squares of the other two sides: verify if \$15^2 = 10^2 + 12^2$.
5. Since the Pythagorean theorem does not hold true for these side lengths, conclude that the triangle is scalene, meaning all sides are different and it is not a right triangle.