The sets of numbers 7, 24, 25 and 9, 40, 41 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain or show why they are Pythagorean triples. Be sure to show your work for each set of triples
To determine if a set of numbers is a Pythagorean triple, we need to check if they satisfy the Pythagorean Theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's start with the set of numbers 7, 24, 25. We need to check if 7^2 + 24^2 = 25^2.
7^2 = 49
24^2 = 576
25^2 = 625
49 + 576 = 625
Since 49 + 576 equals 625, the set of numbers 7, 24, 25 satisfies the Pythagorean Theorem and is a Pythagorean triple.
Now let's move on to the set of numbers 9, 40, 41. We need to check if 9^2 + 40^2 = 41^2.
9^2 = 81
40^2 = 1600
41^2 = 1681
81 + 1600 = 1681
Since 81 + 1600 equals 1681, the set of numbers 9, 40, 41 satisfies the Pythagorean Theorem and is a Pythagorean triple.
Therefore, both sets of numbers 7, 24, 25 and 9, 40, 41 are Pythagorean triples, as they satisfy the Pythagorean Theorem.