Out of the following which is the Pythagorean triplet? (1, 5, 10) (3, 4, 5) (2, 2, 2) (5, 5, 2)

Explanation:-

A Pythagorean triplet is a set of three positive integers such that the sum of the squares of the two smaller integers is equal to the square of the largest integer. In other words, if a, b, and c are three positive integers such that a^2 + b^2 = c^2, then they form a Pythagorean triplet.

Let’s check which one of the given options is a Pythagorean triplet:

Option 1: (1, 5, 10) Here, a = 1, b = 5, and c = 10. So, a^2 + b^2 = 1^2 + 5^2 = 26, and c^2 = 10^2 = 100. Since a^2 + b^2 is not equal to c^2, this is not a Pythagorean triplet.

Option 2: (3, 4, 5) Here, a = 3, b = 4, and c = 5. So, a^2 + b^2 = 3^2 + 4^2 = 9 + 16 = 25, and c^2 = 5^2 = 25. Since a^2 + b^2 = c^2, this is a Pythagorean triplet.

Option 3: (2, 2, 2) Here, a = 2, b = 2, and c = 2. So, a^2 + b^2 = 2^2 + 2^2 = 8, and c^2 = 2^2 = 4. Since a^2 + b^2 is not equal to c^2, this is not a Pythagorean triplet.

Option 4: (5, 5, 2) Here, a = 5, b = 5, and c = 2. So, a^2 + b^2 = 5^2 + 5^2 = 50, and c^2 = 2^2 = 4. Since a^2 + b^2 is not equal to c^2, this is not a Pythagorean triplet.

Therefore, the only Pythagorean triplet among the given options is Option 2: (3, 4, 5).