Determine whether a Triangle with side lengths of 10, 12 and 15 is a Right Triangle

A Right Triangle must satisfy the Converse of the Pythagorean Theorem: a² + b² = c²
From the given side lengths, let a = 10, b = 12, c = 15  (c cannot be less than a or b)
a² + b² = (10)² + (12)²
a² + b² = 100 + 144 = 244
c² = (15)² = 225
a² + b² ≠ c²  (244 ≠ 225)
Therefore, a Triangle with side lengths of 10, 12 and 15 is NOT a Right Triangle
Note: Since a² + b² > c²  (244 > 225), the Triangle is an Acute Triangle