Given Side Lengths: 5, 9, 10
A Right Triangle must satisfy the Converse of the Pythagorean Theorem: a2 + b2 = c2
From the given side lengths, let a = 5, b = 9, c = 10 (c cannot be less than a or b)
a2 + b2 = (5)2 + (9)2
a2 + b2 = 25 + 81 = 106
c2 = (10)2 = 100
a2 + b2 ≠ c2 (106 ≠ 100)
Therefore, a Triangle with side lengths of 5, 9 and 10 is NOT a Right Triangle
Note: Since a2 + b2 > c2 (106 > 100), 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 = 5, b = 9, c = 10 (c cannot be less than a or b)
a2 + b2 = (5)2 + (9)2
a2 + b2 = 25 + 81 = 106
c2 = (10)2 = 100
a2 + b2 ≠ c2 (106 ≠ 100)
Therefore, a Triangle with side lengths of 5, 9 and 10 is NOT a Right Triangle
Note: Since a2 + b2 > c2 (106 > 100), the Triangle is an Acute Triangle
