Which set represents a Pythagorean triple?
A. 27, 38, 42
B. 33, 44, 55
C. 35, 38, 42
D. 68, 72, 81
To determine which set represents a Pythagorean triple, we need to check if it satisfies the Pythagorean Theorem. According to the theorem, in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's check each option:
A. 27, 38, 42:
Checking the theorem:
27^2 + 38^2 = 729 + 1444 = 2173
42^2 = 1764
Since 2173 is not equal to 1764, this set does not represent a Pythagorean triple.
B. 33, 44, 55:
Checking the theorem:
33^2 + 44^2 = 1089 + 1936 = 3025
55^2 = 3025
Since 3025 is equal to 3025, this set represents a Pythagorean triple.
C. 35, 38, 42:
Checking the theorem:
35^2 + 38^2 = 1225 + 1444 = 2669
42^2 = 1764
Since 2669 is not equal to 1764, this set does not represent a Pythagorean triple.
D. 68, 72, 81:
Checking the theorem:
68^2 + 72^2 = 4624 + 5184 = 9808
81^2 = 6561
Since 9808 is not equal to 6561, this set does not represent a Pythagorean triple.
Therefore, the only set that represents a Pythagorean triple is B. 33, 44, 55.