Question

Which of the following represents a Pythagorean Triple? 1 {10, 20, 30} {5, 7, 10} {21, 72, 75} {11, 45, 60}

Answer 1

A Pythagorean Triple is a set of three positive integers that satisfy the Pythagorean theorem. From the given options, only the set {5, 7, 10} and {21, 72, 75} represent Pythagorean Triples.

Step-by-step explanation:

A Pythagorean Triple is a set of three positive integers that satisfy the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Using this information, let's check each of the given sets of numbers to see if they form a Pythagorean Triple:

1. {10, 20, 30}: The sum of the squares of the smaller sides, 10^2 + 20^2 = 500, is not equal to the square of the hypotenuse, 30^2 = 900. Therefore, this set does not represent a Pythagorean Triple.
2. {5, 7, 10}: The sum of the squares of the smaller sides, 5^2 + 7^2 = 74, is equal to the square of the hypotenuse, 10^2 = 100. Therefore, this set represents a Pythagorean Triple.
3. {21, 72, 75}: The sum of the squares of the smaller sides, 21^2 + 72^2 = 5313, is equal to the square of the hypotenuse, 75^2 = 5625. Therefore, this set represents a Pythagorean Triple.
4. {11, 45, 60}: The sum of the squares of the smaller sides, 11^2 + 45^2 = 2286, is not equal to the square of the hypotenuse, 60^2 = 3600. Therefore, this set does not represent a Pythagorean Triple.

From the given options, only the set {5, 7, 10} and {21, 72, 75} represent Pythagorean Triples.