Which set of numbers represents a Pythagorean triple?
6,9,12
7,10,12
16,18,25
27,36,45
Not really looking for a answer but rather how to solve this, or is there a formula?
https://www.mathsisfun.com/pythagorean_triples.html
Pythagorean triples satisfy the equation
... a^2 + b^2 = c^2
... all the values are integers
the most "known" one is 3-4-5
the sum of the squares of the two smaller values, equal the square of the larger value
multiples also work, eg.
... 3-4-5 ... 6-8-10 ...9-12-15 , etc.
Thanks :)
To determine whether a set of numbers represents a Pythagorean triple, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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.
To check if a set of numbers represents a Pythagorean triple, follow these steps:
1. Take the three numbers and label them as a, b, and c.
2. Square each number. Let's call the squares A, B, and C.
3. Check if A + B = C. If they are equal, then the set of numbers represents a Pythagorean triple.
Let's apply this method to the options given:
1. For the set 6, 9, 12:
- A = 6^2 = 36
- B = 9^2 = 81
- C = 12^2 = 144
- A + B = 36 + 81 = 117
- Since 117 is not equal to 144, this set is not a Pythagorean triple.
2. For the set 7, 10, 12:
- A = 7^2 = 49
- B = 10^2 = 100
- C = 12^2 = 144
- A + B = 49 + 100 = 149
- Since 149 is not equal to 144, this set is not a Pythagorean triple.
3. For the set 16, 18, 25:
- A = 16^2 = 256
- B = 18^2 = 324
- C = 25^2 = 625
- A + B = 256 + 324 = 580
- Since 580 is not equal to 625, this set is not a Pythagorean triple.
4. For the set 27, 36, 45:
- A = 27^2 = 729
- B = 36^2 = 1296
- C = 45^2 = 2025
- A + B = 729 + 1296 = 2025
- Since 2025 is equal to 2025, this set is a Pythagorean triple.
Therefore, the correct set of numbers that represents a Pythagorean triple is 27, 36, and 45.