which set represents pythagorean triple?
A.27,38,42
B.33,44,55
C.35,38,42
D.68,72,81
Someone please explain the answer??
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To determine which set represents a Pythagorean triple, we need to check if it satisfies the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's calculate the squares of the lengths of the sides in each set:
A: 27^2 = 729, 38^2 = 1444, 42^2 = 1764
B: 33^2 = 1089, 44^2 = 1936, 55^2 = 3025
C: 35^2 = 1225, 38^2 = 1444, 42^2 = 1764
D: 68^2 = 4624, 72^2 = 5184, 81^2 = 6561
Now, let's check if any set satisfies the Pythagorean theorem by adding the squares of the smaller sides and checking if it equals the square of the largest side:
A: 729 + 1444 = 2173 ≠ 1764 (not a Pythagorean triple)
B: 1089 + 1936 = 3025 = 3025 (Pythagorean triple)
C: 1225 + 1444 = 2669 ≠ 1764 (not a Pythagorean triple)
D: 4624 + 5184 = 9808 ≠ 6561 (not a Pythagorean triple)
Therefore, the set B (33, 44, 55) represents a Pythagorean triple because it satisfies the Pythagorean theorem.