Question

Which set of integers is a Pythagorean triple? 3, 5, 6 5, 12, 13 15, 9, 17 6, 8, 12

Answer 1

"Pythagorean triples" are integer solutions to the Pythagorean Theorem, a2 + b2
5, 12 13

Answer 2

The set of integers which form a Pythagorean triple is:

5,12,13

Explanation:

We are asked to find the set of integers such that they form a Pythagorean triplets.

Three integers a,b,c are said to form a Pythagorean triplets if they satisfy the property:

`c^2=a^2+b^2`

1)

3,5,6

`6^2=36`

and

`3^2+5^2=9+25\\=34\\eq 36`

Hence option: 1 is incorrect.

2)

5, 12, 13

`13^2=169`

and

`5^2+12^2=25+144=169`

This means:

`13^2=5^2+12^2`

Hence, option 2 is correct.

3)

15,9,17

`17^2=289`

Also,

`15^2+9^2=225+81=306\\eq 289`

Hence, option 3 is incorrect.

4)

6,8,12

`12^2=144`

and:

`6^2+8^2=36+64=100\\eq 144`

Hence, option 4 is incorrect.