Question

Which triples are Pythagorean Triples?

a) 8,15,17
b) 1, √3, 2
c) 9,12,16
d) 8,11,14
e) 20,21,29
f) 30,40,50

Answer 1

To determine which triples are Pythagorean Triples, we need to check if they satisfy the Pythagorean Theorem. The Pythagorean Triples are a) 8, 15, 17; e) 20, 21, 29; and f) 30, 40, 50.

Step-by-step explanation:

To determine which triples are Pythagorean Triples, we need to check if they satisfy the Pythagorean Theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. For example, in the triple (a, b, c), if a² + b² = c², then it is a Pythagorean Triple.

Let's check each given triple:

1. 8, 15, 17: 8² + 15² = 64 + 225 = 289 = 17², so it is a Pythagorean Triple.
2. 1, √3, 2: 1² + (√3)² = 1 + 3 = 4 ≠ 2², so it is not a Pythagorean Triple.
3. 9, 12, 16: 9² + 12² = 81 + 144 = 225 ≠ 16², so it is not a Pythagorean Triple.
4. 8, 11, 14: 8² + 11² = 64 + 121 = 185 ≠ 14², so it is not a Pythagorean Triple.
5. 20, 21, 29: 20² + 21² = 400 + 441 = 841 = 29², so it is a Pythagorean Triple.
6. 30, 40, 50: 30² + 40² = 900 + 1600 = 2500 = 50², so it is a Pythagorean Triple.

Therefore, the Pythagorean Triples are a) 8, 15, 17; e) 20, 21, 29; and f) 30, 40, 50.