Given Side Lengths: 12, 13, 17
A Right Triangle must satisfy the Converse of the Pythagorean Theorem: a2 + b2 = c2
From the given side lengths, let a = 12, b = 13, c = 17 (c cannot be less than a or b)
a2 + b2 = (12)2 + (13)2
a2 + b2 = 144 + 169 = 313
c2 = (17)2 = 289
a2 + b2 ≠ c2 (313 ≠ 289)
Therefore, a Triangle with side lengths of 12, 13 and 17 is NOT a Right Triangle
Note: Since a2 + b2 > c2 (313 > 289), 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 = 13, c = 17 (c cannot be less than a or b)
a2 + b2 = (12)2 + (13)2
a2 + b2 = 144 + 169 = 313
c2 = (17)2 = 289
a2 + b2 ≠ c2 (313 ≠ 289)
Therefore, a Triangle with side lengths of 12, 13 and 17 is NOT a Right Triangle
Note: Since a2 + b2 > c2 (313 > 289), the Triangle is an Acute Triangle
