If 9, 12, 15 is a Pythagorean Triple, which of the following could also be a Pythagorean Triple? a) 5,7,9 b) 17, 20, 23 c) 36, 48, 60 d) 19, 22, 25

Question

asked Sep 20, 2023 150k views

1 Answer

SUPARNA SOMAN · Answer 1 · 2023-09-25T23:48:19+0000

Answer:

c) 36, 48, 60

Explanation:

A Pythagorean Triple is a set of positive integers (a, b, c) that follows the rule:

$\boxed{a^2+b^2=c^2}$

where a < c and b < c.

It always consists of:

When a and b are both even, c is even.

When one of a and b is odd and the other is even, c is odd.

(5, 7, 9) cannot be a Pythagorean Triple since it consists of all odd numbers.

(17, 20, 23) is not a Pythagorean Triple since:

$\implies 17^2+20^2=23^2$

$\implies 289+400=529$

$\implies 689 \\eq 529$

(36, 48, 60) is a Pythagorean Triple since:

$\implies 36^2+48^2=60^2$

$\implies 1296+2304=3600$

$\implies 3600=3600$

(19, 22, 25) is not a Pythagorean Triple since:

$\implies 19^2+22^2=25^2$

$\implies 361+484=625$

$\implies 845\\eq 625$