Given Side Lengths: 9, 4.5, 10.5
A Right Triangle must satisfy the Converse of the Pythagorean Theorem: a2 + b2 = c2
From the given side lengths, let a = 4.5, b = 9, c = 10.5 (c cannot be less than a or b)
a2 + b2 = (4.5)2 + (9)2
a2 + b2 = 20.25 + 81 = 101.25
c2 = (10.5)2 = 110.25
a2 + b2 ≠ c2 (101.25 ≠ 110.25)
Therefore, a Triangle with side lengths of 4.5, 9 and 10.5 is NOT a Right Triangle
Note: Since a2 + b2 < c2 (101.25 < 110.25), 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 = 4.5, b = 9, c = 10.5 (c cannot be less than a or b)
a2 + b2 = (4.5)2 + (9)2
a2 + b2 = 20.25 + 81 = 101.25
c2 = (10.5)2 = 110.25
a2 + b2 ≠ c2 (101.25 ≠ 110.25)
Therefore, a Triangle with side lengths of 4.5, 9 and 10.5 is NOT a Right Triangle
Note: Since a2 + b2 < c2 (101.25 < 110.25), the Triangle is an Obtuse Triangle
