Given Side Lengths: 12, 14, 15
A Right Triangle must satisfy the Converse of the Pythagorean Theorem: a2 + b2 = c2
From the given side lengths, let a = 12, b = 14, c = 15 (c cannot be less than a or b)
a2 + b2 = (12)2 + (14)2
a2 + b2 = 144 + 196 = 340
c2 = (15)2 = 225
a2 + b2 ≠ c2 (340 ≠ 225)
Therefore, a Triangle with side lengths of 12, 14 and 15 is NOT a Right Triangle
Note: Since a2 + b2 > c2 (340 > 225), the Triangle is an Acute Triangle
A Right Triangle must satisfy the Converse of the Pythagorean Theorem: a2 + b2 = c2
From the given side lengths, let a = 12, b = 14, c = 15 (c cannot be less than a or b)
a2 + b2 = (12)2 + (14)2
a2 + b2 = 144 + 196 = 340
c2 = (15)2 = 225
a2 + b2 ≠ c2 (340 ≠ 225)
Therefore, a Triangle with side lengths of 12, 14 and 15 is NOT a Right Triangle
Note: Since a2 + b2 > c2 (340 > 225), the Triangle is an Acute Triangle
