1. Which set represents a Pythagorean triple?
A. 27, 38, 42
B. 33, 44, 55**
C. 35, 38, 42
D. 68, 72, 81
Your answer is correct.
33² + 44² = 1089 + 1936 = 3025 = 55²
correct
To determine which set represents a Pythagorean triple, we need to check if the three numbers in the set satisfy the Pythagorean theorem, which states that in a right 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 set:
A. 27, 38, 42
To determine if this is a Pythagorean triple, we need to check if 27^2 + 38^2 = 42^2
27^2 + 38^2 = 729 + 1444 = 2173
42^2 = 1764
Since 27^2 + 38^2 does not equal 42^2, this set is not a Pythagorean triple.
B. 33, 44, 55
To determine if this is a Pythagorean triple, we need to check if 33^2 + 44^2 = 55^2
33^2 + 44^2 = 1089 + 1936 = 3025
55^2 = 3025
Since 33^2 + 44^2 equals 55^2, this set (33, 44, 55) represents a Pythagorean triple.
C. 35, 38, 42
To determine if this is a Pythagorean triple, we need to check if 35^2 + 38^2 = 42^2
35^2 + 38^2 = 1225 + 1444 = 2669
42^2 = 1764
Since 35^2 + 38^2 does not equal 42^2, this set is not a Pythagorean triple.
D. 68, 72, 81
To determine if this is a Pythagorean triple, we need to check if 68^2 + 72^2 = 81^2
68^2 + 72^2 = 4624 + 5184 = 9808
81^2 = 6561
Since 68^2 + 72^2 does not equal 81^2, this set is not a Pythagorean triple.
Therefore, the correct set representing a Pythagorean triple is B. 33, 44, 55.