Given Side Lengths: 10, 12, 20
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 = 20 (c cannot be less than a or b)
a2 + b2 = (10)2 + (12)2
a2 + b2 = 100 + 144 = 244
c2 = (20)2 = 400
a2 + b2 ≠ c2 (244 ≠ 400)
Therefore, a Triangle with side lengths of 10, 12 and 20 is NOT a Right Triangle
Note: Since a2 + b2 < c2 (244 < 400), the Triangle is an Obtuse 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 = 20 (c cannot be less than a or b)
a2 + b2 = (10)2 + (12)2
a2 + b2 = 100 + 144 = 244
c2 = (20)2 = 400
a2 + b2 ≠ c2 (244 ≠ 400)
Therefore, a Triangle with side lengths of 10, 12 and 20 is NOT a Right Triangle
Note: Since a2 + b2 < c2 (244 < 400), the Triangle is an Obtuse Triangle
